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Atom-Probe Tomography

  • Thomas F. KellyEmail author
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

This chapter provides an overview of the current state of atom-probe tomography ( ). The history of APT is recounted so that the reader may put the many modern developments in context. It is noted that atom-probe tomography has the highest spatial resolution among analytical techniques (\({\mathrm{0.2}}\,{\mathrm{nm}}\)), and it has the highest absolute analytical sensitivity (single atoms), a unique combination. The fundamentals of APT, including the operative physics, performance metrics, and hardware configurations, are discussed. Before examining the many benefits that may be realized in APT, however, its limitations such as image distortions and specimen failures are discussed in full. Specimen preparation procedures for most materials are explained. A comprehensive overview of the many materials applications including metals, ceramics, semiconductors, and organics is provided. Finally, there is a look toward the future to see where the technique is headed.

Keywords

atom-probe tomography time-of-flight mass-spectrometry physics of field evaporation mass resolving power laser pulsing geometry of atom probes detector technology reconstruction algorithms 

15.1 The History of APT

The genesis of the atom probe can be traced to at least the early twentieth century, when an experimental demonstration of the existence of atoms in crystals (and of the wave nature of x-rays) was achieved in 1912 by von Laue [15.1, 15.2, 15.3]. The theory of the wave nature of matter had been put forward by de Broglie in 1923 [15.4], and a theory of the focusing action of an electromagnetic coil was formulated by Busch [15.5] in 1927. At the Technical University of Berlin, two projects had started in 1930 which pursued implications of these developments. A graduate student named Ernst Ruska, working under Professor Max Knoll, had started experiments on the lensing action of magnetostatic fields on electron beams to test Busch's theory, and with an eye toward making an electron microscope. Another student named Erwin Müller, working under Professor Gustav Hertz, was using high electrostatic fields applied to material surfaces to extract electron beams. It would be very interesting to know whether either sensed that these efforts at the same institution would eventually lead to the first images of atoms: Müller using field ion microscopy in 1955 [15.6, 15.7] and Crewe et al using scanning transmission electron microscopy (STEM) in 1970 [15.8]. As we will see later in this chapter, these two techniques will likely be joined again into a single instrument.

Müller first demonstrated that electron emission could be achieved by applying high fields to metal needles [15.9]. It was straightforward to show analytically that an electric field of less than one volt across an atom (\(\approx{\mathrm{2}}\,{\mathrm{\AA{}}}={\mathrm{2\times 10^{-10}}}\,{\mathrm{m}}\)), which is \(> {\mathrm{10^{9}}}\,{\mathrm{V/m}}\), would be sufficient to remove a valence electron from an atom. How can one create such high electric fields? Electro-mechanics could be used to show that a few thousand volts applied to a needle with an apex radius of \({\mathrm{10^{-6}}}\,{\mathrm{m}}\) is sufficient to create such electric fields. If we take two electrically conductive concentric spheres and apply a potential between them, then the electric field on the surface of the inner sphere is simply \(E=V/R\), where \(E\) is the magnitude of the electric field, \(V\) is the potential difference between the spheres, and \(R\) is the radius of the inner sphere (Fig. 15.1a,ba). If we take a hemisphere on the end of a needle opposed by a large plate (Fig. 15.1a,bb), the field is a bit lower, \(E=V/(kR)\), where \(k\) is about 3. Note that it does not matter how close the outer electrode is in this formulation (except for the needle geometry when the counter electrode gets within \(\approx{\mathrm{1000}}R\)).

Fig. 15.1a,b

Creation of high electric fields. (a) Electric field on the inner sphere surface for concentric spheres with a potential between them. (b) Electric field on the apex of a needle with a spherical endcap

Müller made sharp metal needles by electropolishing wires (Sect. 15.4) and made field electron emission measurements in a blown glass vacuum system (Fig. 15.2a-ca). In due course, Müller began to consider if there was any structure in the field emission patterns. The counter electrode was converted into a fluorescent screen and the field of field electron (emission) microscopy ( ) was born [15.9]. It was possible to see structure in the emission pattern that was consistent with the crystallographic symmetry present in the specimen [15.10] (Fig. 15.2a-cc). Field emission patterns are essentially a map of the work function variations with crystal orientation. Over the next decade, work continued to improve the quality and resolution of the patterns. With the steady improvement in quality, there developed a great desire to see whether the technique could be improved all the way to resolving atoms. Müller pursued this ideal for several years into the 1940s. His work was severely interrupted by World War II. Indeed, he almost died of starvation in Germany during that time, since scientists who did not cooperate with the Nazi regime were ostracized.

Fig. 15.2a-c

Field (electron) emission microscopy (FEM). (a) Glass vacuum chamber used by Müller to make field electron emission measurements, (after [15.11]). (b) Schematic of a FEM. (c) FEM pattern of tungsten \(\langle 110\rangle\), from [15.10]

After the war, Müller was invited to emigrate to the USA, and he chose Pennsylvania State University, as the locale reminded him of his home region. Here, his work took a turn. One of the techniques used to improve the resolution of FEM images was to clean the tip by reversing the polarity. This seemed to remove adsorbed gases and yielded sharper FEM images. At some point, Müller and his group considered whether there was any structure in the projection of the desorbed gases, much like FEM images. They intentionally introduced a gas at a slightly elevated pressure to ensure a supply of gas atoms on the needle (Fig. 15.3a-ca), and indeed found detailed structure in the projected pattern (Fig. 15.3a-cb). Since the electric field was now oriented to remove positive charge from the specimen, they knew that these gas atoms must be positively ionized. By 1951, they published their first field ion microscope ( ) images [15.12]. Almost from the start, these FIM images showed greater detail than the FEM images. The obvious exciting question was whether the technique could be improved to resolve atoms. Two key experimental exigencies were eventually understood to make a substantial difference: a) smoothing and cleaning the needle apex by sufficient field evaporation to create a field-evaporated end form, and b) cooling the specimen to cryogenic (liquid nitrogen) temperatures to freeze out atomic motion. There were false starts and some luck, but eventually, on October 11, 1955, Müller and his graduate student Kanwar Bahadur recorded the first images of atoms ever [15.6, 15.7] (Fig. 15.3a-cc). Melmed has provided a summary of the events leading up to this momentous occasion [15.13].

Fig. 15.3a-c

Field ion microscopy (FIM). (a) Schematic of a FIM, where the gas supply is usually an inert gas at about \({\mathrm{10^{-3}}}\,{\mathrm{Pa}}\). (b) The first FIM images showed ledges of a tip surface. From [15.12]. (c) The first atomic-resolution images of any type ever recorded were made on October 11, 1955, by Bahadur and Müller [15.6, 15.7], as recounted by Melmed [15.13]. Example image in (c) reprinted from [15.14], with the permission of AIP Publishing

You might think that the first humans ever to image atoms would have received the highest possible accolades. Unfortunately, it did not happen. Many people familiar with the characters at the time believe that Ruska and Müller were being considered for the Nobel Prize in the late 1970s. However, Müller died unexpectedly in 1977. Ruska later shared the 1986 Nobel Prize with Binnig and Rohrer of scanning tunneling microscope fame.

FIM was an enormous success, and it led to some notoriety for Müller and his group. For the next decade, FIM was used by a growing community of scientists to image such things as defects in materials: vacancies, interstitials, dislocations, cavities, and grain boundaries (Fig. 15.4a,b) [15.15, 15.16]. One can imagine that after a decade of atomic-scale imaging, the practitioners of FIM had to be wondering whether they could do more than just image atoms on the surface: could they also identify them? In FIM, one can observe a static field ion image and see it change as specimen atoms evaporate in the high electric field. Müller's group again took the initiative and sought to apply mass spectroscopy techniques to the field-evaporated atoms. Doug Barofsky, a graduate student in the group, was tasked with adapting a magnetic sector mass spectrometer to the field-evaporated atoms. Before long, Barofsky realized that time-of-flight ( ) mass spectroscopy would likely be the more successful method [15.17]. Müller assigned another graduate student, John Panitz, to this task. Note that not only did Panitz need to sort out a ToF configuration, but he also had to figure out how to detect single atoms! It had never been done before. Within a year, Panitz had built an instrument that could image a tip with FIM, position a particular atom inside an aperture on the image, pulse the electric field on the specimen to initiate an evaporation event, and detect the atom (ion) and its flight time (Fig. 15.5a-d) [15.18]. By analogy with the electron microprobe, which had gained prominence in the 1960s, they dubbed this instrument the atom probe. Because it utilized a field ion microscope, it was often referred to as an atom-probe field ion microscope ( ). Within months of their first public disclosures, other groups around the world had replicated the feat. Atom probes sprang up in Pittsburgh at US Steel under Sid Brenner, in Oxford at the University of Oxford under George Smith, at Cornell University under David Seidman, and at the Technical University of Chalmers in Gothenburg under Hans Nordén.

Fig. 15.4a,b

Field ion images of (a) a screw dislocation intersecting a surface of a metal specimen. Note the spiral curve of FIM spots emanating counterclockwise from the center. Reprinted from [15.16]. By permission of Oxford University Press http://www.oup.com. (b) Field ion micrograph of boron-doped nickel aluminide (\(\mathrm{Ni_{3}Al}\)). The bright dots are individual boron atoms that have segregated to a grain boundary (arrows). After [15.15]

Fig. 15.5a-d

The atom-probe field ion microscope (APFIM). (a) Schematic of the probe hole geometry for APFIM. The specimen may be tilted such that either the yellow atom or the red atom passes through the probe hole to the detector. (b) Electron multiplier detector in the first atom probe adapted by John A. Panitz to detect single atoms. Provided by and used with permission of John A. Panitz. (c) Overall schematic of the first APFIM. (d) John A. Panitz at the first APFIM instrument at Pennsylvania State University. Note the use of quartz tubing for the specimen and gimbal, and stainless steel for the flight tube. Provided by and used with permission of John A. Panitz

The first atom probes were one-dimensional ( ); that is, the data structure consisted of detected atoms in a sequence which represented depth into the specimen. Figure 15.6 is an example of the application of an atom probe to the study of chromium distribution in an Fe-\({\mathrm{45}}\,{\mathrm{at.\%}}\) Cr alloy. One can discern the composition of each of the phases in a material at the atomic scale. The first commercial atom probe was built in the late 1970s by Vacuum Generators in cooperation with the group at the University of Oxford under the leadership of George Smith (Fig. 15.7a,ba) [15.19]. One of these VG FIM100 instruments that was originally at the Massachusetts Institute of Technology and Northwestern University is on display across from gate B12 at Chicago O'Hare International Airport. A second commercial atom probe was designed by Bob Waugh at Applied Microscopy (Fig. 15.7a,bb).

It was not long before the desire arose to detect not just the few ions which passed through a small aperture, but to detect all the atoms field-evaporated from the specimen. Panitz took a key step in this direction when he developed the \({\mathrm{10}}\,{\mathrm{cm}}\) atom probe [15.20], followed by the imaging atom probe ( ) [15.21]. The \({\mathrm{10}}\,{\mathrm{cm}}\) atom probe was the first truly three-dimensional () atom probe, since it could detect all (with \({\mathrm{100}}\%\) detection efficiency) of the ions of a given species by time gating for that species' flight time on a large detector (Fig. 15.8). Now, for example, all the carbon atoms in a phase could be seen over an area. The third dimension of the image is the sequence of evaporation events which coincide with depth into the specimen as in the one-dimensional atom probe. Alas, the IAP could not map all atom types at the same time. This required detector technology, yet to be invented, that could record each atom's hit position on the detector and its hit time.

Fig. 15.6

One-dimensional composition profile across \(\upalpha\)\(\upalpha^{\prime}\) phase boundaries in an Fe-\({\mathrm{45}}\,{\mathrm{at.\%}}\) Cr alloy. From [15.22]

Fig. 15.7a,b

The first commercial atom probes were one-dimensional. (a) The Vacuum Generators VG FIM100 APFIM installed at the University of Oxford. Courtesy of Alfred Cerezo and George D.W. Smith , Department of Materials, Oxford University. The toroidal Poschenrieder lens was used for energy compensation to improve mass resolving power to about 2000. This picture shows this instrument fitted with a position-sensitive detector on what was originally the imaging atom probe port (below Alfred Cerezo's right hand). Note the electrical feedthroughs on the port for the wedge-and-strip detector. (b) The Applied Microscopy APFIM 220  [15.23]. This instrument sports a reflectron energy-compensating device. Reprinted from [15.23], with permission from Elsevier

Fig. 15.8

(a) Schematic of the \({\mathrm{10}}\,{\mathrm{cm}}\) atom probe and (b) photograph of the \({\mathrm{10}}\,{\mathrm{cm}}\) atom probe. Photo courtesy of John A. Panitz. (c) Time-gated field evaporation image of tungsten\({}^{3+}\) and tungsten\({}^{4+}\) ions surrounding the \(\mathrm{110}\) pole. Note the large field of view and three-dimensionality of the data, which is a portent of later three-dimensional atom probes. Reprinted from [15.21], with the permission of AIP Publishing

In the early days of the atom probe, pulsing of the evaporation event was done exclusively by pulsing the electric field applied to the specimen. A specimen must have high electrical conductivity for this form of pulsing, and so all the early work in atom probes was done on metals. By the late 1970s, there was growing interest in finding a way to pulse nonmetals, and experiments with thermal pulsing were attempted with pulsed laser heating by Kellogg and Tsong [15.24]. These experiments succeeded, and eventually, as recounted below, laser pulsing became the dominant mode of pulsing by the year 2010. All manner of materials can now be atom-probed regardless of their electrical conductivity.

An attempt to overcome the limitations of the IAP was made by Michael Miller in the mid-1980s [15.25]. This instrument was never completed, but it did spark interest in the idea. The first working atom probe to map all detected atoms in three dimensions did not surface until the late 1980s when Alfred Cerezo et al adapted a position-sensitive detector (shown in Fig. 15.7a,ba) to a VG FIM100 [15.26, 15.27], and called it the position-sensitive atom probe ( ) (Fig. 15.9). The images were awe-inspiring. Here now was an instrument that could map the atomic composition in three dimensions with atomic-scale resolution. The community dubbed these instruments three-dimensional atom probes ( ). The group at the Université de Rouen soon developed a 3-DAP called the tomographic atom probe ( ) [15.28, 15.29], which generated similarly spectacular images (Fig. 15.10). Eventually, the Oxford group founded a company, Kindbrisk (later called Oxford NanoScience ), to commercialize the PoSAP (Fig. 15.11). The Rouen group developed a relationship with CAMECA SAS in Paris to commercialize the TAP (Fig. 15.12). By 1995, both companies were selling 3-DAPs at the rate of about one per year. Interest in the technique grew.

Fig. 15.9

(a) Schematic of the position-sensitive atom probe (PoSAP) built on a VG FIM100. (b) First images from the PoSAP of an AlNiCo magnet showing Fe-rich, Al-rich, and Cu-rich phases. From [15.27]

Fig. 15.10

(a) Schematic of tomographic atom probe. After [15.29]. (b) Atom map of NiAl specimen showing only Al atoms with an isoconcentration surface surrounding the \(\mathrm{Ni_{3}Al}\) \(\mathrm{L1_{2}}\) ordered phase. Note the Al {001} are visible in the ordered phase. Reprinted from [15.30], with permission from Elsevier

Fig. 15.11

The first commercial position-sensitive atom probe (PoSAP) was built by Kindbrisk , Ltd. This photograph is an ECOPoSAP which had later been fitted with a gas handling system (rightmost table in the photo) for research on catalysis. Courtesy of Alfred Cerezo and George D.W. Smith, Department of Materials, Oxford University

Fig. 15.12

Photograph of the commercial tomographic atom probe (TAP) manufactured by CAMECA with help from the Université de Rouen

As spectacular as the images from 3-DAPs were, there were some serious challenges. Firstly, the data were generated at a rate of about one atom per second. A million-atom data set, which is small for materials studies, would take over a week to collect. The largest images recorded were a couple of million ions. The mass resolving power was limited to about \(\mathrm{200}\) by the fact that field pulsing was used, which introduces an energy spread on the evaporated ions. The field of view, about \(15{-}20\,{\mathrm{nm}}\) in diameter, was not very large. In a time-of-flight instrument, if you move the detector toward the source, the image size increases but the flight times decrease, and the mass resolution degrades. About this time, Osamu Nishikawa presented a concept he called the scanning atom probe ( ) [15.31, 15.32] (Fig. 15.13). The intent was to make it possible to analyze sharp protrusions that might occur or be fabricated on a surface by applying the high electric field from a conical aperture. This concept had the potential to radically alter the way specimens were prepared for atom probe. Indeed, this has come to pass, as illustrated in Sect. 15.4. Nishikawa built an instrument where the aperture was scanned across a surface with a high applied potential and a detector at the ready whenever ions were field-evaporated from a sharp protrusion.

Fig. 15.13

Schematic of the scanning atom probe (SAP) that used a funnel-shaped extraction electrode close to the specimen to extract ions into a standard atom probe geometry. After [15.31]

At that time, the author of this chapter was pursuing ways to improve the 3-DAP and was struck by the potential of Nishikawa's idea to effect these improvements. The low data rate of 3-DAPs at the time was a consequence of two factors: (a) because the position-sensitive detectors in use had poor multihit detection, evaporation events were intentionally limited to low probability (\(\approx 1\) event per \(\mathrm{100}\) pulses) to keep the errors due to multiple hits low (\(\approx 1\) error per \(\mathrm{10^{4}}\) pulses), and (b) the technology used to pulse the field was reed switches, which were limited to producing about \(\mathrm{100}\) pulses per second. These two factors resulted in a detection rate of about one atom per second. Because of the proximity of the counter electrode in a SAP, the electric field was notably higher than with a remote counter electrode. This made it possible to lower the amplitude of the voltage pulse required, which made it possible to achieve pulse repetition rates several orders of magnitude greater using solid-state pulse generators. Because the voltage was lower, we could use post-acceleration of the ions to reduce the relative energy spread of the evaporated ions. This resulted in a direct improvement in the mass resolution. This improvement in mass resolution was independent of field of view, so we could open the field of view. The net effect of all these improvements was a 3-DAP that had a data collection rate of a million atoms per minute (\(\approx{\mathrm{20000}}\,{\mathrm{atoms/s}}\)), with a mass resolving power of \(\mathrm{500}\) over a field of view of \(> {\mathrm{100}}\,{\mathrm{nm}}\). The largest data sets have reached a billion ions from a single specimen. The local electrode was the key to these improvements, and the instrument was called the local-electrode atom probe, or LEAP [15.33, 15.34] (Fig. 15.14).

Fig. 15.14

Picture of beta LEAP installed at the Oak Ridge National Laboratory

Laser pulsing was first applied to 3-DAPs by Cerezo et al [15.35, 15.36] and later by Gault et al [15.37] and Bunton et al [15.38]. Laser pulsing has been a crucial component of the success of APT in the past decade, since it opened the possibility for analysis of materials with low electrical conductivity: i. e., semiconductors and insulators. Examples of these applications can be found below.

In 1998, the author founded Imago Scientific Instruments Corporation to commercialize the LEAP. The first instrument was purchased and shipped in 2003 to Michael Miller at Oak Ridge National Laboratory. That first shipped instrument (shown in Fig. 15.14) has just recently been retired from service. By the time you are reading this chapter, over \(\mathrm{100}\) LEAPs will have been shipped (in 2017). The field has grown markedly, as evidenced by the growth in the number of publications per year, which correlates with the number of instruments shipped (Fig. 15.15a,b). Imago was acquired in 2010 by Ametek, Inc., and was made part of CAMECA SAS . There is one other commercial instrument which is being developed by a group headed by Guido Schmitz at the Universität Stuttgart. This instrument is designed to be attached to a focused ion beam ( ) instrument so that specimens may travel directly from the FIB to the atom probe without being exposed to the atmosphere.

Fig. 15.15a,b

Growth in the field of APT as illustrated by (a) the number of publications listing atom-probe tomography versus year of publication. (b) Relative number of publications by application area. After [15.39]

15.2 Fundamentals of APT

15.2.1 Physics of Field Evaporation

The most fundamental requirement for operating an atom probe is the creation of a very high electric field on the surface of a material. These fields must be high enough to tear atoms apart. As Müller posited and learned in the 1930s, accomplishing this task is surprisingly straightforward. In the case of two electrically conducting spheres with a potential \(V\) between them (Fig. 15.1a,ba), the electric field \(E\) on the surface of the inner sphere is simply
$$E=\frac{V}{kR}\;,$$
(15.1)
where \(R\) is the radius of the inner sphere, and \(k=1\) for the concentric sphere geometry. Note that the radius of the outer sphere \(d\) does not matter. Clearly, the case of two concentric spheres is not experimentally straightforward to create. However, if the inner electrode is a needle with a hemispherical endcap, and it is opposed by a planar electrode as shown in Fig. 15.1a,bb, the electric field on the needle apex is reduced by a factor \(k\), which has a typical value of about \(3{-}5\).

Electric fields of \({\mathrm{10^{9}}}\,{\mathrm{V/m}}\) are needed to induce field electron emission. If \({\mathrm{3000}}\,{\mathrm{V}}\) is taken to be a convenient high voltage for a laboratory setting, then \(R\) must be \(\mathrm{10^{-6}}\) (\({\mathrm{1}}\,{\mathrm{\upmu{}m}}\)). Müller set about making metal needles with this radius of curvature at the apex. As you will see in Sect. 15.4, electropolishing methods on metal wires can readily make such geometries.

The flux of evaporated ions from a sharp needle can be written as [15.40]
$$R_{n}(E,T)=N_{\text{hr}}k_{n}(E,T)=N_{\text{hr}}A_{n}\mathrm{e}^{-\frac{Q_{n}(E)}{k_{\mathrm{B}}T}}\;,$$
(15.2)
where \(R_{n}\) is a flux of field-evaporated ions of charge \(n\mathrm{e}^{+}\) in units of \(\mathrm{ions/s}\), where \(\mathrm{e}^{+}\) is the charge of a proton, \(T\) is the specimen apex temperature, \(k_{n}\) is the rate constant for evaporation of high risk atoms of charge \(n\) in units of \(\mathrm{s}^{-1}\), \(N_{\text{hr}}\) is the number of high risk atoms exposed to the high electric field on the surface of the needle, \(A_{n}\) is the rate constant prefactor of an ion of charge \(n\), \(Q_{n}\) is the field-dependent activation barrier for field evaporation of an ion of charge \(n\), and \(k_{\mathrm{B}}\) is the Boltzmann constant. Note that \(R_{n}\) increases exponentially with increases in electric field and temperature. This fact will be important in how pulsing of the field evaporation is accomplished for time-of-flight measurements (explained below).

Creation of ions by field evaporation requires electric fields about one order of magnitude greater than field electron emission. Thus, for applied potentials of about \({\mathrm{3000}}\,{\mathrm{V}}\) on the specimen apex, radii of about \({\mathrm{10^{-7}}}\,{\mathrm{m}}\) (\({\mathrm{100}}\,{\mathrm{nm}}\)) are required. Such specimen geometries are readily created, as discussed in Sect. 15.4. The temperature of the specimen apex is also important in atom-probe tomography, since atomic diffusion on the surface would ideally be avoided if possible during an atom probe experiment. At room temperatures, atoms on most surfaces would be moving around too much on the timescales relevant for atom-probe tomography (a few ms). For this reason, atom-probe tomography is generally performed at homologous temperatures of a few percent.

15.2.2 Time-of-Flight Mass Spectrometry

Though the first concept for an atom probe was based on a magnetic sector mass spectrometer [15.17, 15.41], time-of-flight spectrometry has been used exclusively for mass identification in atom-probe tomography since. The first ToF atom probe was built by Müller, Panitz, and McLane [15.18, 15.42], as shown in Fig. 15.5a-d. To measure time of flight, the field evaporation event must be constrained to a time window on the order of a nanosecond. This is accomplished by pulsing the field evaporation rate. As noted above, either the electric field may be pulsed (known as voltage pulsing or field pulsing) or the specimen apex temperature may be pulsed (known as thermal pulsing or laser pulsing when lasers are used). The total flight time is determined by when the ion hits the detector.

The total flight time for ions depends on several key operating parameters. Since the electric field gradient is very high near the specimen apex, a field-evaporated ion gains most of its speed in the first few percent of the flight path. For this reason, a simple first-order estimate of the functional dependence of the time of flight can be derived by assuming constant speed and setting the final kinetic energy equal to the total potential energy gain
$$neV=\frac{1}{2}mv^{2}\;,$$
(15.3)
where \(n\) is the charge state of the ion which may assume integer values, \(e\) is the electric charge of an electron, \(m\) is the mass of the ion, and \(v\) is the final speed of the ion. With the speed constant over the distance traveled \(L\), and rearranging, the mass-to-charge state ratio may be determined
$$ \frac{m}{n}=\frac{2eV}{L^{2}}t^{2}\quad\text{ or }$$
(15.4)
$$ t=L\sqrt{\dfrac{\frac{m}{n}}{2eV}}\;,$$
(15.5)
where \(v=L/t\) has been used. A full electrostatic solution is required for a more accurate relationship, but this approximation is good to a few percent in most cases. Typical flight times for \({\mathrm{100}}\,{\mathrm{mm}}\) flight path lengths and \({\mathrm{10}}\,{\mathrm{kV}}\) operating voltage for a mass/charge state ratio of \({\mathrm{30}}\,{\mathrm{Da}}\) (\(\mathrm{{}^{30}Si^{+}}\) or \(\mathrm{{}^{60}Ni^{2+}}\)) would be about \({\mathrm{400}}\,{\mathrm{ns}}\). To measure this flight time with good resolution, a timing uncertainty for the ions must be on the order of a nanosecond or better. The field evaporation event must be pulsed on this timescale, and the timing electronics must be able to resolve subnanosecond flight times.

15.2.3 Mass Resolving Power

The purpose of mass spectrometry is to distinguish between different atomic (isotopic) species in a material. The mass resolving power ( ) is commonly invoked as a means for assessing the quality of atom probe mass spectra and this ability to correctly distinguish the mass peaks in a spectrum [15.43]. MRP can also be used for drawing comparisons between mass spectra collected on different atom probe instruments or under different acquisition conditions. The MRP of a spectrometer will also impact the detection limit for a given ion species, since a \((m/n)\) peak with a higher MRP will have a better signal-to-noise ratio than a peak with lower MRP [15.44].

The measure of the peak width in a mass spectrum, \(\partial m\), is one of the most important metrics by which mass spectrometer performance is measured. The peak width must be defined at some reference height, such as full width at half maximum ( ), full width at tenth maximum ( or FW.1M), or full width at 100th maximum (FW.01M). Usually, the width is expressed by normalizing it to the mass of the peak, \(\partial m/m\), which is called the mass resolution and is a number less than unity. Alternatively, the inverse of the mass resolution, \(m/\partial m\), is called the mass resolving power and is a number greater than unity.

The mass resolution will be approximated by the uncertainty in the measurement of \((m/n)\). From (15.4), using the methods of propagation of uncertainties, the uncertainty in \((m/n)\) can be expressed in the following form
$$\frac{\partial m}{m}=\sqrt{\left(\frac{\partial V}{V}\right)^{2}+\left(\frac{2\partial t}{t}\right)^{2}+\left(\frac{2\partial L}{L}\right)^{2}}\;,$$
(15.6)
where \(\partial V\) is the uncertainty associated with power supply instabilities, inaccuracies in the voltage measurement, and the energy spread of the field-evaporated ions; \(\partial t\) is the timing uncertainty associated with the ToF departure spread and the timer hardware; and \(\partial L\) is the flight path length uncertainty [15.45, 15.46, 15.47]. During laser pulsing experiments, the energy spread of the majority of the ions is expected to be small (\(\approx{\mathrm{1}}\,{\mathrm{eV}}\)), and the stability of modern power supplies is high enough that, to a first approximation, \(\partial V\) can be assumed to be very small [15.45, 15.46, 15.48]. Further, for regions near the center of the detector, the flight path length uncertainty, \(\partial L\), is small [15.46, 15.47]. Substituting \(\partial V=0\) and \(\partial L=0\) into (15.6) and using (15.5) produces the following expression for the MRP [15.46, 15.47],
$$\text{MRP}=\frac{m}{\partial m}=\frac{t}{2\partial t}=\frac{1}{2\partial t}\frac{L}{\sqrt{2eV}}\sqrt{\frac{m}{n}}\;.$$
(15.7)
Hence, the MRP is proportional to the ToF, \(t\), and therefore any acquisition conditions that increase the ToF without increasing \(\partial t\) should also improve the MRP. It follows that the MRP should be higher for higher \((m/n)\) peaks in the mass spectrum and that MRP will degrade as the acquisition voltage increases [15.46, 15.47]. Further, from (15.7) it can be seen that the MRP is proportional to \(L\), to \(\sqrt{(m/n)}\), and to \(\sqrt{V^{-1}}\) indicating that the MRP must be specified for a particular flight path length, mass-to-charge state ratio, and acquisition voltage [15.46, 15.47].

A typical mass spectrum from a multicomponent metal alloy taken on a LEAP is shown in Fig. 15.16a,b. If the energy spread for the ions in the spectrum were negligible and the peak width was limited by the timing electronics, the peaks would have a symmetric shape. During field pulsing, however, the ion creation event can occur at different points during the rise and fall of the applied field. The result is a broadening of the peaks in the mass spectrum due to a range of potential energy gains, and hence a range in time of flight. The peaks are also asymmetric, because there are more ions with energy loss than gain (broadened to the high \(m/n\) side).

Fig. 15.16a,b

Typical mass spectrum from a LEAP recorded in field pulsing mode. (a) Spectrum from \(m/n\approx{\mathrm{3}}\) to \({\mathrm{100}}\,{\mathrm{Da}}\). (b) A zoomed-in range of the mass spectrum from \(m/n\approx{\mathrm{24}}\) to \({\mathrm{34}}\,{\mathrm{Da}}\) where many of the doubly charged transition metals are found

15.2.4 Reflectron

The energy spread in field pulsing limits the achievable MRP to about \(\mathrm{100}\). To achieve higher MRP, energy-compensating devices were applied to the atom probe. The first is known as the Poschenrieder lens named after its inventor [15.49, 15.50]. It is a toroidal electrostatic sector with a time-focused output at \(163.2^{\circ}\) of bend. More energetic ions penetrate deeper into the bending fields of the sector, which lengthens their flight time compared with lower-energy ions so that all ions arrive at the detector at the same time. There were about six FIM100 sold by Vacuum Generators (Fig. 15.7a,ba), and it was the only commercial instrument to use a Poschenrieder. A reflectron [15.51] (Fig. 15.17a,ba) accomplishes the same feat with less complexity. An electrostatic mirror is used to deflect ions by close to \(180^{\circ}\). Higher-energy ions penetrate deeper into the retarding electric field, which takes extra flight time. The location of the detector is designed to correspond to the location where the ions are time-focused. After VG discontinued the FIM100 in about 1984, the principal designer of the FIM100, Bob Waugh, left VG and started Applied Microscopy. He designed a one-dimensional reflectron-based atom probe (Fig. 15.7a,bb). Applied Microscopy sold two of these instruments in the mid 1980s.

Fig. 15.17a,b

Schematic of the reflectron geometries. A reflectron used in a one-dimensional ( ) atom probe would work on a narrow beam of ions as suggested by the 1-D detector. (a) Wide-angle reflectron used in the ECOPoSAP. (b) Curved wide-angle reflectron developed by Oxford NanoScience. This curved reflectron is used in CAMECA atom probes (models 3000 HR and XHR, 4000 HR and XHR, 5000 R and XR, and Eikos)

At the start of the three-dimensional atom probes, the MRP was modest (\(<200\)). Cerezo et al [15.52] adapted a reflectron to the PoSAP to create what they called the energy-compensated PoSAP ( ), as presented in Fig. 15.11 and shown schematically in Fig. 15.17a,ba. The ECoPoSAP achieved MRP of \(\mathrm{800}\) over a \({\mathrm{20}}\,{\mathrm{nm}}\)-diameter field of view, which was a substantial improvement over prior instruments. An ECoTAP was also developed in the late 1990s by the Université de Rouen and CAMECA. When larger fields of view (\({\mathrm{150}}\,{\mathrm{nm}}\) diameter) eventually became available in the LEAP with MRP of \(\mathrm{500}\) or more in the early 2000s, Panayi [15.53, 15.54] devised a large-field-of-view reflectron by curving the electric fields (Fig. 15.17a,bb). The curved electric fields convert a divergent beam of ions coming from the specimen into a convergent beam, which means that a small detector can still subtend a large field of view with energy compensation. Oxford NanoScience did not sell an instrument with this reflectron because it was acquired by Imago in 2006 before a product was introduced. However, this curved reflectron has been used since in all reflectron-based 3-DAPs made by Imago and CAMECA. This curved reflectron makes it possible to have MRP of \(> {\mathrm{1000}}\) in both field pulsing and thermal pulsing. This is an advantage in multi-user environments where a range of specimen types are encountered. The mass spectrum in Fig. 15.16a,b was recorded on a LEAP 4000 XHR in field pulsing mode.

In thermal pulsing, the applied electric field is (nominally) constant and the peaks are almost symmetric about their midpoint. An MRP of about three times the peak separation is typically needed for good peak separation. Thus, at \(m/n\) of \({\mathrm{30}}\,{\mathrm{Da}}\), an MRP of at least \(\mathrm{100}\) FWHM is desirable for resolving peaks separated by \({\mathrm{1}}\,{\mathrm{Da}}\). Because the charge state can be as high as \(n=3\) or 4, peaks can end up separated by only \(1/6\,\text{Da}\) or less. An MRP of \(\mathrm{600}\) at \(m/n\) of \({\mathrm{30}}\,{\mathrm{Da}}\) would be desirable in this case. Modern atom probes typically deliver MRP of about \(\mathrm{1000}\) or better at \(m/n\) of \({\mathrm{30}}\,{\mathrm{Da}}\) (Fig. 15.16a,b). The peaks are Lorentzian in shape all the way to the noise floor. There are several peaks (some highlighted) that are separated by only \(1/6\,\text{Da}\) (Fig. 15.16a,bb). The high MRP eliminates most peak overlaps for improved compositional determinations. With the signal confined to a narrow peak, the signal-to-noise ratio is improved, which leads to better sensitivity.

15.2.5 Pulse Fraction

The first atom probe instruments all relied on field pulsing. This was the simplest to accomplish and remains a technique that is used to this day. A potential range of between 3 and \({\mathrm{15}}\,{\mathrm{kV}}\) is common in modern atom probes. Nanosecond-duration voltage pulses of the order of \({\mathrm{10}}\,{\mathrm{kV}}\) are extremely difficult to produce, especially at high repetition rates. Instead of pulsing the entire potential applied to the specimen, a pulsed voltage is applied on top of a standing voltage. If \({\mathrm{10}}\,{\mathrm{kV}}\) is needed to induce a sensible field evaporation rate, then a voltage of \({\mathrm{8}}\,{\mathrm{kV}}\) will result in a field evaporation rate that is many orders of magnitude lower. Given this fact, a standing voltage of \({\mathrm{8}}\,{\mathrm{kV}}\) could be maintained with negligible evaporation events, and a pulse of \({\mathrm{2}}\,{\mathrm{kV}}\) in \({\mathrm{1}}\,{\mathrm{ns}}\) can be applied to induce a momentary and sensible evaporation event. This fractional field pulsing is achieved by choosing a pulse fraction in the control software, defined as the ratio of the pulse amplitude to the total applied voltage at the peak of the pulse, and increasing the base voltage until evaporation events are detected. In this way, an operator chooses a pulse fraction, and a computer increases the base voltage until a certain evaporation probability is realized. This evaporation probability, the number of ions detected per pulse, is referred to as the detection ratio and is typically on the order of \(E-3{-}E-1\) in modern instruments.

The pulse fraction was investigated by some researchers [15.55, 15.56]. It was recognized that a low pulse fraction can be problematic because atoms may field evaporate between pulses when the field is still relatively high, and therefore they are lost to time-of-flight measurements. Lost atoms will never be good, but they can be especially deleterious if atoms of distinct species are lost differentially. The result would be determination of an incorrect composition. A high pulse fraction is great for data integrity, but difficult or impossible to achieve technologically. Typical pulse fractions used are between \(\mathrm{10}\) and \({\mathrm{25}}\%\), with \(15{-}20\%\) being the usual range [15.55].

In addition to the technical difficulty in creating nanosecond voltage pulses of a few kilovolts in amplitude, it is a challenge to obtain the full voltage amplitude to propagate to the specimen apex. The circuit impedance between the specimen and the voltage source must support gigahertz (nanosecond pulses) time constants. A typical specimen geometry in an atom probe will have a capacitance to the world of a few picofarads. This says that specimens must have a conductivity in the low metallic range (\({\mathrm{10^{2}}}\,{\mathrm{S}}\)) to have an impedance low enough to support the gigahertz pulse. For this reason, atom probe by field pulsing was limited to metal specimens almost exclusively in the first three decades of the technique.

15.2.6 Laser Pulsing

To overcome this limitation, Kellogg and Tsong [15.24] investigated thermal pulsing to pulse field evaporate materials of low electrical conductivity. Their first efforts were on intrinsic silicon, which has a high resistivity. They showed clear advantages of laser pulsing, including independence of the specimen electrical conductivity and high achievable mass resolution (due to low energy spread and constant applied electric field). Liu and Tsong [15.57] especially showed that very high mass resolution could be achieved by conducting experiments with \(L={\mathrm{8}}\,{\mathrm{m}}\) so that a very large \(t\) was realized for a constant \(\partial t\), (15.6). Though their experiments were a clear success, it was more than two decades before thermal pulsing by laser became mainstream in atom-probe tomography, largely due to limitations in laser technology. The first laser-pulsed 3-DAP was built by Liddle et al [15.58] and used for studies of compound semiconductors. This work was also hampered by laser technology at the time. The pulse-to-pulse energy variation was too great in the early lasers, and specimens would be hit by excessive energy on an occasional pulse, which would destroy the specimen.

Eventually, efforts were restarted with better laser technology in the mid-2000s [15.37, 15.38, 15.59]. Some of the early focus was on trying to achieve athermal pulsing: that is, using the electric field of the photon pulse to increase the applied electric field on the specimen. Investigations seeking to clarify thermal versus athermal pulsing with a laser eventually showed that thermal pulsing dominates the pulsed field evaporation with a laser [15.38, 15.60, 15.61]. It may still be that athermal pulsing of field evaporation can be achieved in some situations, but it has yet to be demonstrated experimentally. There have been reviews of laser pulsing that explored the mechanism of pulsing in detail [15.62, 15.63]. The question of how photon energy is absorbed when the band gap of the specimen is greater than the laser photon energy has been vexing the field for some time. In brief, the high electric field can induce surface states that absorb photons of energy lower than the bulk band gap. It is also likely that there are impurity gap states created by ion implantation during ion milling of the specimen. The interested reader is referred to the review articles cited above [15.62, 15.63].

15.2.7 Geometry of Atom Probes

Today, over \({\mathrm{90}}\%\) of all operating atom probes are LEAPs. To understand this instrument, we should first consider a remote-electrode atom probe, or REAP, which represents almost all the remaining atom probe instruments and was the first type of atom probe made. Figure 15.18a,b illustrates the essential geometry needed to operate an atom probe. The counter electrode can be located macroscopic distances (many millimeters or more) away from the specimen. The counter electrode could be the detector or screen, but most REAPs have a separate electrode located near the specimen as shown in Fig. 15.18a,ba. The electrode aperture is typically several millimeters in diameter, and its actual separation distance from the specimen does not affect the electric field on the specimen in any significant way.

Fig. 15.18a,b

Schematic comparison of atom probe geometries. (a) Remote-electrode atom probe ( ). (b) Local electrode atom probe ( ). The scanning atom probe ( ) and LEAP both feature a counter electrode that is a key component of the operation. \(L\) is the flight path length to the center of the detector and \(R\) is the radius of the detector. \(V_{\text{tot}}\) is the total accelerating voltage of the system, \(V_{\text{ext}}\) is an extraction voltage, \(V_{\text{pa}}\) is a post-acceleration voltage that can range from zero to greater than \(V_{\text{ext}}\), and \(V_{\mathrm{p}}\) is a voltage pulse that is the time-varying component of dynamic fields. In most commercial instruments, the counter electrode is a small aperture of about \({\mathrm{40}}\,{\mathrm{\upmu{}m}}\) diameter. Ion optics can be used to bend the ion rays toward the axis so that longer flight path lengths (or smaller detectors) can be used for better mass resolving power

When an atom probe experiment is conducted with a needle-shaped specimen, the needle starts out sharp and gradually becomes more blunt (\(R\) increases) as it evaporates. The voltage on the needle apex must therefore increase during the experiment as the specimen blunts to maintain the evaporation field on the specimen; see (15.1). There are two main consequences of this blunting action:
  1. 1.

    For a given material (hence a given evaporation field), the maximum voltage available on any instrument determines the maximum bluntness that can be evaporated.

     
  2. 2.

    The projection magnification decreases during the experiment, and therefore the field of view increases, as the specimen becomes more blunt.

     
Since in a remote-electrode atom probe, the field of view is directly related to the evaporation voltage for a given material, it was common to refer to a specimen that had been evaporated at \({\mathrm{12}}\,{\mathrm{kV}}\) as a 12 kV tip. If that specimen were introduced into another REAP, it would begin evaporating at \({\mathrm{12}}\,{\mathrm{kV}}\). Typical early atom probes were designed with a maximum operating voltage of \({\mathrm{20}}\,{\mathrm{kV}}\). Thus, the maximum field of view for a given material in a REAP was directly tied to the maximum operating voltage. The local electrode geometry had a big impact on this fact.

15.2.8 Rationale for a LEAP

As the electrode approaches the specimen, as shown in Fig. 15.19, the electric field on the specimen apex at a constant applied potential increases. The effect is small until the separation approaches length scales comparable to the scale of the specimen apex radius (sub-\(\mathrm{\upmu{}m}\)), i. e., when the effect becomes local. The standard specimen-to-counter electrode separation in a LEAP is about \({\mathrm{40}}\,{\mathrm{\upmu{}m}}\), at which the field enhancement is a factor of \(\mathrm{2}\). This is intentionally the diameter of the aperture in a LEAP such that an angular acceptance angle of about one radian is achieved. Higher field enhancement factors can be pursued but at a price. We know that specimens will fracture under the very high hydrostatic stress that exists for a tip at a high electric field. The hydrostatic stress in the near-apex region varies as the square of the applied electric field and approaches the cohesive strength of materials during evaporation. Any small weakness or flaw can lead to rupture. Smaller-entrance apertures on the local electrode intercept more debris from fractures, and this reduces the usable life of the local electrodes. Though \({\mathrm{10}}\,{\mathrm{\upmu{}m}}\) local electrode apertures would give a threefold field enhancement factor, they will also fail more frequently. Since the fabrication and certification process for local electrodes is expensive, the practical solution is a compromise between field enhancement and lifetime.

Fig. 15.19

Effect of counter electrode proximity on the field factor and hence the electric field at the specimen apex. Typical LEAP operating condition: \(\approx 2\times\) field enhancement, \(\approx{\mathrm{40}}\,{\mathrm{\upmu{}m}}\) aperture

You might be wondering what benefit is to be gained from localized field enhancement? There are at least four important consequences:

Novel Specimen Geometries

Nishikawa et al [15.31, 15.32] ushered in the second revolution in atom-probe tomography with their suggestion of using of a small, funnel-shaped counter electrode. In their vision, this counter electrode would be scanned across a surface that contained a protrusion which might be sharp enough to field evaporate under the electric field applied. They dubbed this the scanning atom probe (SAP). It is important to note that prior to their work, all atom probe specimens were long (\({\mathrm{10}}\,{\mathrm{mm}}\)) metal needles. Now, the overwhelming majority of atom probe specimens are short (\({\mathrm{100}}\,{\mathrm{\upmu{}m}}\)) microtips on a flat surface. Kelly et al picked up on this concept for novel specimen geometries and also explored the consequences for instrument performance improvements [15.33, 15.34]. Cerezo et al [15.64, 15.65] also pursued this concept.

With a \({\mathrm{40}}\,{\mathrm{\upmu{}m}}\) diameter aperture at the apex of a cone-shaped electrode, the region of high electric field can be localized to a very small volume on the order of (\({\mathrm{40}}\,{\mathrm{\upmu{}m}}\))\({}^{3}\). When there is an array of field evaporation tips, this makes it possible to localize the high fields to a single emitter. This fact is utilized in the SAP approach where a fracture surface, for example, could become a source of many individually addressable sharp points. In the LEAP geometry, this fact has been used to construct microtip arrays such as in Fig. 15.20a-d, where each microtip can be run in the LEAP without affecting adjacent microtips. In this manner, a single microtip array coupon can be used to introduce as many as 36 experiments into the instrument (18 shown in Fig. 15.20a-da). The implications of this fact for design of experiment have been very important for the development of atom-probe tomography.

Fig. 15.20a-d

Microtip coupons for LEAP. (a) SEM image of a microtip coupon with \(\mathrm{18}\) microtips. There are three fiducial structures on the surface also. (b) A solid model of a specimen carrier (puck) with a microtip coupon mounted. Coupons are available with either (c) presharpened microtips or (d) flat-top microtips

Typically, when a material or specimen type is being run for the first time in an atom probe, one must explore the operating space to establish conditions of pulse fraction, laser energy, specimen temperature, and such that lead to success. Since specimen introduction into ultrahigh vacuum systems can take hours, the ability to introduce an entire experiment's worth of specimens in one exchange can greatly accelerate the process and even enable appropriate experimental investigation.

Larger Field of View

A LEAP operating with a \(2\times\) field enhancement gives a \(2\times\) larger field of view (\(4\times\) on the area) at any given voltage. The field of view in atom probes is especially important because, whereas in other microscopies the field of view is just what can be observed at any given time without moving the specimen, in atom probes, the field of view determines the analyzed volume. The features of interest must be present in the analyzed volume or another specimen must be run. In early three-dimensional atom probes, the field of view was about \({\mathrm{20}}\,{\mathrm{nm}}\) in diameter. If the specimen thickness that was run was \({\mathrm{20}}\,{\mathrm{nm}}\), the analyzed volume would be about \({\mathrm{7\times 10^{3}}}\,{\mathrm{nm^{3}}}\). The feature density would need to be greater than \([1/({\mathrm{7\times 10^{3}}})]{\mathrm{nm^{-3}}}={\mathrm{1.4\times 10^{-4}}}\,{\mathrm{nm^{-3}}}={\mathrm{1.4\times 10^{23}}}\,{\mathrm{m^{-3}}}\) to be observed in a small number of specimens. Through a combination of field enhancement and larger detectors and greater analysis speed (see next section Higher-Repetition-Rate Voltage Pulsing, below), a LEAP may analyze a \({\mathrm{100}}\,{\mathrm{nm}}\) field of view for a \({\mathrm{100}}\,{\mathrm{nm}}\) depth. This is \({\mathrm{8\times 10^{5}}}\,{\mathrm{nm^{3}}}\) or a number density of \({\mathrm{1.2\times 10^{-6}}}\,{\mathrm{nm^{-3}}}={\mathrm{1.2\times 10^{21}}}\,{\mathrm{m^{-3}}}\) required if they are to be observed in a small number of observations. There is a 100-fold greater chance of observing a feature in a LEAP data set than in the earlier three-dimensional atom probes.

Higher-Repetition-Rate Voltage Pulsing

Before the emergence of commercial laser pulsing of atom probes in 2005, voltage pulsing was the principal method of pulsing. Since a typical pulse fraction should be at least \({\mathrm{15}}\%\), a specimen operating at \({\mathrm{15}}\,{\mathrm{kV}}\) would require a \({\mathrm{2250}}\,{\mathrm{V}}\) pulse in a nanosecond time frame. Historically, this was accomplished with mercury-wet reed switches which could deliver the voltage pulse amplitude in this time frame. However, these electromechanical devices could only be pulsed at a maximum repetition rate of about \({\mathrm{100}}\,{\mathrm{Hz}}\). Until about 2002, this was the fastest pulsing that existed for atom probes. Since the position-sensitive detectors at the time could not correctly encode more than one hit event at a time, it was necessary to keep the probability of ion evaporation events low (about 1 event per \(\mathrm{10^{2}}\) pulses) to keep the probability of two events per pulse very low (about 1 event per \(\mathrm{10^{4}}\) pulses). Thus, the first generation of three-dimensional atom probes managed to collect about \({\mathrm{1}}\,{\mathrm{atom/s}}\) (about \(\mathrm{10^{5}}\) atoms per day). There was a high incentive to find a way to speed things up. Multihit capabilities for position-sensitive detectors have not improved much since this time, so the only way to achieve large gains was through increasing the repetition rate of the pulses.

The achievable repetition rate for solid-state electronic voltage pulse generators (of nanosecond duration) can be \(\mathrm{10^{4}}\) pulses per second for amplitudes of a few hundred volts. Through a combination of developing a higher electronic pulse amplitude capability and a higher repetition rate, a pulser with \(\mathrm{5\times 10^{5}}\) pulses per second and a \({\mathrm{1500}}\,{\mathrm{V}}\) amplitude was developed at Imago Scientific Instruments. In combination with the field enhancement factor of \(\mathrm{2}\), this enabled \({\mathrm{20}}\%\) pulse fractions to be achieved in voltage pulsing for \({\mathrm{7.5}}\,{\mathrm{kV}}\) tips, which would be \({\mathrm{15}}\,{\mathrm{kV}}\) tips on a REAP. At \({\mathrm{1}}\%\) detection rate, this translated into a data collection rate of \({\mathrm{5\times 10^{3}}}\,{\mathrm{atoms/s}}\), an increase of more than three orders of magnitude over prior generations of atom probes.

Mass Resolution Improvement

The mass resolution achieved in voltage pulsing is generally limited by energy spread of the ions, (15.6), where \(\partial V\) is the largest component. This energy spread is an intrinsic component of the fact that the accelerating field in the time-of-flight measurement is time-varying (pulsed), and depending on when during the rise and fall of a pulse an evaporation event occurs, differing amounts of energy are acquired by the ion [15.66, 15.67]. It is the voltage magnitude, not the electric field magnitude, that determines the amount of energy gained. When there is field enhancement, the lower voltage required leads to a lower energy spread acquired, i. e., voltage spread is a repeatable fraction of the voltage pulse magnitude which is reduced by field enhancement effects. Thus, when there is a twofold field enhancement, there is a twofold reduction in voltage spread. If the ions are post-accelerated to higher voltage, then the \(\partial V/V\) term is reduced by a factor of \(\mathrm{2}\). This fact has been used in the design of the LEAP to increase the mass resolving power. In the first LEAPs shipped, the MRP in voltage pulsing was higher than \(\mathrm{400}\), whereas a comparable REAP had MRP of \(\mathrm{200}\). Though this aspect of local electrode operation has not been widely exploited yet, it remains a prospect for future instrument improvement. If larger field enhancement factors are pursued, then post-acceleration could offer a path to higher MRP, at least in voltage pulsing.

The sum of all these improvements is an instrument that is far better matched to the needs of microscopy at the atomic scale. The LEAP was a major advance in atom-probe technology and has been referred to by the author as the second revolution in atom-probe tomography [15.68], the first revolution being the advent of three-dimensional atom probes with position-sensitive detectors [15.26], which itself followed the advent of three-dimensional atom probes [15.20].

15.2.9 Detector Technology

The detector is the heart of an atom probe. As shown in Fig. 15.18a,b, regardless of the atom probe geometry, the detector plays the essential role of recording the ion hit positions and their arrival times. There is an extensive list of essential features which must be met by any detector technology, and failure to meet any one is reason to reject the technology. A partial list of such features is shown in Table 15.1. The minimum acceptable standard for many of these parameters has evolved markedly since the early days. For example, pixelated charge-coupled device (CCD) cameras have been used on some three-dimensional atom probes to detect ions when \({\mathrm{10}}\,{\mathrm{ions/s}}\) was the norm, but their relatively low achievable frame rates became a severe limitation with the advent of much greater data rates like \({\mathrm{10^{4}}}\,{\mathrm{ions/s}}\).

Table 15.1

Essential features of position-sensitive detectors for atom-probe tomography

Feature

Typical value

Minimum acceptable value

Pixel resolution

\({\mathrm{700}}\times{\mathrm{700}}\)

\({\mathrm{400}}\times{\mathrm{400}}\)

Timing resolution

\({\mathrm{40}}\,{\mathrm{ps}}\)

\({\mathrm{1}}\,{\mathrm{ns}}\)

UHV compatible

Yes

Yes

Diameter size (mm)

\(\mathrm{80}\)

\(\mathrm{30}\)

Pulse pair resolution (ns)

\(<{\mathrm{2}}\)

\(<{\mathrm{5}}\)

Detection efficiency

\({\mathrm{80}}\%\)

\({\mathrm{30}}\%\)

Detection efficiency variation with \(Z\)

None

Monotonic and stable

Maximum mass (Da)

\(\mathrm{500}\)

\(\mathrm{300}\)

Multihit resolution

Resolve most double hits

Multihits not resolved

Gain

\(> {\mathrm{4\times 10^{5}}}\)

\(> {\mathrm{10^{5}}}\)

Maximum count rate (\(\mathrm{s^{-1}}\))

\(\mathrm{10^{6}}\)

\(\mathrm{10^{3}}\)

Lateral resolution (\(\mathrm{\upmu{}m}\))

\(\mathrm{100}\)

\(\mathrm{300}\)

Minimum ion energy (keV)

\(\mathrm{2}\)

\(\mathrm{4}\)

The detector technology used universally today is a microchannel plate (MCP ) coupled with a delay-line anode ( ) [15.69]. There are many good reasons for this technology's widespread use, and there are some limitations. MCPs have high gain (\(\approx{\mathrm{10^{3}}}\) per plate), have fast response (\(<{\mathrm{1}}\,{\mathrm{ns}}\) pulse duration), adequate throughput (can handle \(\approx{\mathrm{10^{6}}}\) events), high lateral spatial resolution (\(\approx{\mathrm{10}}\,{\mathrm{\upmu{}m}}\)), uniform gain for atom probe applications (\(> {\mathrm{2}}\,{\mathrm{keV}}\) ions, mass \(<{\mathrm{500}}\,{\mathrm{Da}}\)), and good uniformity across the face. Atom probes generally use a pair of MCPs to achieve gains of about \(\mathrm{10^{6}}\). Their principal shortcoming is that they have a finite detection efficiency of \(\leq{\mathrm{80}}\%\).

Delay-line anodes (DLA) were adopted in the late 1990s for atom-probe tomography [15.70, 15.71] and have been the exclusive detector technology since. A major advantage for them is that they readily provide both a hit position and an arrival time signal as an intrinsic aspect of their operation. Their pulse pair resolution is adequate but not stellar. When two ions hit the detector simultaneously, they must be separated in space by a large fraction of the detector width (\({\mathrm{30}}\%\) or more) or they will not be resolved as separate hits. Multiple ion hits must be separated in time or space (since distance is time on a delay line) by more than the pulse pair resolution if they are to be discerned as two hits. In field evaporation, it is not uncommon for identical isotopes to emerge on a surface next to each other and evaporate with a time between events that is less than the pulse pair resolution. These are the multihit events that are not correctly identified as such, and lead to lost information. If different isotopes of the same element evaporate simultaneously, they will have different flight times and they are generally resolved. When a double hit is not resolved but is counted as one atom, that species is undercounted, and the composition determination is skewed (unless all atom types have the same skew, which is not likely) [15.72, 15.73, 15.74].

This multihit limitation of MCP-DLA detectors has another insidious side effect. Atom probe operation is controlled to minimize the probability of multiple evaporation events in any given pulse. This amounts to keeping the probability of one evaporation event per pulse low (\(\leq{\mathrm{10^{-2}}}\)) so that the probability of double hits is very low (\(\leq{\mathrm{10^{-4}}}\)). If we could evaporate atoms at one or even \(\mathrm{100}\) atoms per pulse and correctly encode them, there would be a gain of two to four orders of magnitude in the data collection rate possible. We do not know for sure that specimens will survive at these high evaporation rates, but it would be nice to find out. Prior to the high-speed operation of today's LEAPs, there was concern expressed in the community that high-repetition-rate pulsing would lead directly to premature specimen fracture, but that has not been the case. In fairness, higher evaporation rates per pulse will require higher electric fields applied and the hydrostatic stress in the specimen increases as the square of the applied electric field. Thus, specimens will be under higher stresses when running at higher evaporation rates, and most specimens are already on the hairy edge of remaining intact.

In Sect. 15.6, new detector technologies that are being pursued are described that might overcome some or all of these limitations.

15.2.10 Vacuum Requirements

Any gas in a vacuum is a potential source of field ions just as in FIM. Field ions contaminate the atom probe data (timed events) and may just become part of the background (untimed events). During atom probe operation, we would ideally like to have perfect vacuum. Ultrahigh vacuum ( ) is generally called for in atom probe operation. Modern instruments are designed for ultrahigh vacuum with stainless steel chambers, ConFlat metal seals and a thermal bake at least \({\mathrm{140}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\) or higher. Three chamber systems are used (analysis chamber, intermediate chamber, and airlock) to minimize the disruption of the vacuum in the analysis chamber from specimen exchanges. Turbo pumps are used on the intermediate chamber and airlock. Ion pumps or turbo pumps are used on the analysis chamber.

Typical operating pressure for the main analysis chamber is in the low \(\mathrm{10^{-8}}\)Pa (\({\mathrm{10^{-10}}}\,{\mathrm{mbar}}\)) range or better. Even with this UHV approach, there is a discernible influence of the analysis chamber pressure on the background in a mass spectrum. Since over \({\mathrm{90}}\%\) of the residual gas in a vacuum system such as these is hydrogen [15.77], it is the main gas observed to influence the mass spectrum. Mass peaks at 1 (\(\mathrm{H^{+}}\)), 2 (\(\mathrm{H_{2}^{+}}\)) and even 3 (\(\mathrm{H_{3}^{+}}\)) Da can be seen in spectra when there is no expectation of hydrogen in the specimen. The source of this hydrogen is outgassing from the stainless-steel chambers. There is interest in eliminating this source of hydrogen because, at best, it muddles, and at worst, it destroys the ability of atom-probe tomography to map hydrogen in real materials. Despite these limitations, there have been successful efforts to map hydrogen in materials by using deuterium charging in steel to observe differences in the deuterium signal (from the steel) with the hydrogen signal (from the vacuum system) [15.75, 15.78] (Fig. 15.21a-ea,b), and by observing high levels of hydrogen that spatially correspond with hydride phases [15.76] (Fig. 15.21a-ec–e).

Fig. 15.21a-e

Hydrogen mapping in materials with APT. 3-D elemental maps of (a) deuterium-uncharged (reprinted from [15.75], with permission from Elsevier) and (b) deuterium-charged specimens of a TiC-bearing steel after annealing (reprinted from [15.75], with permission from Elsevier). The arrow in (a) indicates the analysis direction. In (ce) a Nd-Fe-B permanent magnet material containing a platelet-shaped \(\mathrm{NdH_{2}}\) phase is observed to have the expected stoichiometry for the platelets (reprinted from [15.76], with permission from Elsevier). (c) SEM image of the atom probe specimen, (d) 3-D atom maps of Nd and H showing the platelet structure, and (e) a composition profile along the long axis of the rectangular parallelepiped and normal to a platelet shown in (d)

15.2.11 Reconstruction Algorithms

In the early days of the three-dimensional atom probe (early 1990s), the community was in awe of the beautiful images of materials. We could see atomic planes in the images, which was very reassuring that atomic resolution was achieved. It was equally amazing that the very simple algorithm used to reconstruct images from raw data [15.79] worked as well as it did. This algorithm assumes that the specimen shape is a spherical endcap on a conic frustum, and ions are geometrically projected onto the planar detector. The model was later improved and corrected to remove a small-angle approximation [15.80], but this basic algorithm remains the basis of reconstruction today. There have been efforts to improve various aspects of APT reconstruction [15.81, 15.82, 15.83, 15.84, 15.85, 15.86, 15.87, 15.88], and new methods have been proposed and explored [15.89]. However, real tips are not spherical [15.90, 15.91, 15.92, 15.93, 15.94, 15.95, 15.96], so reconstructed images contain distortions wherever the specimen apex shape is not spherical. It is important to note that these distortions are a failure of the post-experimental reconstruction method and not some physical limitation. They are caused by ignorance; that is, a lack of knowledge of the shape of the evaporating surface, and therefore a lack of knowledge of the correct projection law to use in reconstruction.

There are two basic approaches to rectifying this lack of accuracy in reconstruction, endogenous ones and exogenous ones. There is some hope that the atom probe data themselves (endogenous correction) contain sufficient information to correct the distortions [15.97]. Efforts to determine the specimen apex shape during the atom probe experiment which would enable a more accurate reconstruction (exogenous correction) are being pursued presently (see discussion below and [15.100, 15.98, 15.99]). Until such approaches succeed, atom probe images will contain distortions. The causes of these distortions can be faceting at low index poles on single crystal specimens, called monophase distortions, as in Fig. 15.22a-c, or differences in evaporation fields for different phases, called polyphase distortions, shown in Fig. 15.23a-d. The distortions that accrue in the reconstructed image can range from subnanometer to several nanometers. In extreme cases (Fig. 15.23a-db,c), ions cross and cannot then be correctly reconstructed in space as information is lost.

Fig. 15.22a-c

Range of possible evaporating surfaces for a simple structure. (a) Monophase material with a spherical endcap shown. Amorphous materials might form such an end form. Note that the endcap is not tangentially continuous where it transitions to the conic frustum. (b) A more realistic representation of a crystalline specimen with faceting at low index poles. (c) Field evaporation histogram from \(\langle 100\rangle\) aluminum. The histogram would be smoothly varying in intensity across its surface if there were no faceting. The zone axes and zone lines are visible because there is a low hit density at these locations caused by faceting of closely packed atomic planes

Fig. 15.23a-d

Range of possible evaporating surfaces based on differences in evaporation field, \(E_{\text{ev}}\), for a polyphase specimen. (a) A specimen with a modest difference in evaporation field between the two phases (\(E_{\text{ev}\,\upalpha}> E_{\text{ev}\,\upbeta}\)). (b) A specimen with a large difference in evaporation field between the two phases (\(E_{\text{ev}\,\upalpha}\gg E_{\text{ev}\,\upbeta}\)). This is a schematic illustration of the case where a concave surface has been formed and ion crossing is expected as a result. (c) TEM image of an actual specimen of \(\mathrm{SiO_{2}}/\text{Si}/\mathrm{SiO_{2}}\) where a severe concave surface has formed by differential field evaporation. Reprinted from [15.96], with permission from Elsevier. (d) TEM image of an actual specimen of \(\text{Si}/\mathrm{SiO_{2}}/\text{Si}\) where the opposite result occurs. Reprinted from [15.96], with permission from Elsevier

It is important to note that despite such distortions, there is a very large body of experimental data recorded and analyzed every day for which these distortions are either small or not important. We all want to perfect image reconstruction in atom-probe tomography, but until that happens, there is much gain being realized by the technique, and it can address a wide spectrum of atomic-scale applications with high spatial resolution and analytical sensitivity. The example applications below are a testimony to this fact.

15.3 Limitations and Strengths of APT

Any scientific experiment has its limits of sensitivity and repeatability. It is particularly important to understand these limitations in the case of atom-probe tomography because, given the simple nature of atom probe operation, it is natural and tempting to look at an atom map and consider that it is free from artifacts. A review of the potential sources of artifacts in APT is a good primer for a careful experimentalist.

15.3.1 Limitations of APT

Specimen Fracture

For many forms of microscopy and microanalysis, obtaining an image or analysis is a simple matter of placing the specimen in the instrument and recording the information. This is especially true for light microscopy, for example, but it is not always the case for atom probes. Huge strides have been made in the past decade with materials that had not historically been amenable to atom probe analysis. Semiconductors, ceramics, organics, and even teeth and bone have all been studied recently. These results have shown that most any type of material will stand up to the process of field evaporation and can yield data. However, it is not always possible to simply prepare a specimen and expect to capture good data. There are many examples of materials that run well, but it took some investigation of operating parameters to find a combination of specimen preparation geometry, specimen base temperature, laser pulsing or voltage pulsing conditions, detection ratio, and such to find reliable conditions that produced good results. There are also examples of structures, usually ones with many different phases and possibly weak interfaces, that fracture before any useful data can be recorded.

Material Types Affect Reconstructions

Also, as a community we have learned that the simplest atomic structures like those of metals run reliably and produce the most readily understood results. The evaporating entity is usually a monatomic ion and its placement in the reconstruction is straightforward. As the atomic structure gets more complex, like those of oxides or ceramic materials with many atoms per unit cell of the crystal, the field evaporation process and corresponding mass spectra become more complex. The evaporating entity may be a polyatomic ion that can be identified uniquely and correctly in the mass spectrum. In the limit of very large molecular materials like organic structures, the evaporating entity may be a subunit of the molecular structure, but there may be ambiguity in the identity since multiple combinations of atoms could account for the mass of the entity. Furthermore, though there has been work done to account for a molecular ion's orientation and precise placement in a reconstruction [15.102, 15.103], this type of reconstruction consideration is not yet well established. As progress is made on improving the spatial positioning of all species in a reconstruction, the orientation of the entity in the reconstruction will become a necessity.

Image Distortions

It is tempting to think of atom probe reconstructions as showing every atom correctly positioned. The spatial resolution can be excellent in some locations in some structures. Spatial resolution has been assessed by means of a real-space interatomic-spacing averaging technique known as spatial distribution maps ( ) [15.101, 15.104]. Figure 15.24a-c shows an SDM of tungsten where the {110} of body-centered cubic () are evident. The averaged atom positions are distributed about a point, and the full width at half maximum of the distribution can be taken as a measure of the spatial resolution achieved [15.105, 15.106].

Fig. 15.24a-c

Spatial distribution map (SDM) of a tungsten specimen where the average crystal structure (bcc) is clearly discernible. The \(z\)-axis is aligned with the analysis direction. (a) Side view of an atom map of W where the {110} are visible. (b) SDM which shows the statistical presence of {110} in the structure. (c) SDM looking in the analysis (\(z\)) direction where a \(\langle 110\rangle\) arrangement of atomic sites is clearly visible. From [15.101], reproduced with permission

Using this metric, the image in Fig. 15.24a-ca shows \({\mathrm{150}}\,{\mathrm{pm}}\) spatial resolution. Gault et al [15.107] used an alternative definition which had been advocated by Vurpillot et al [15.108] for achievable spatial resolution and showed values better than \({\mathrm{200}}\,{\mathrm{pm}}\) resolution laterally and \({\mathrm{60}}\,{\mathrm{pm}}\) resolution in depth in aluminum. That is the good news. The bad news is that this spatial resolution is not uniform throughout the entire image. In the direction of low index crystal orientations, the atomic planes are closely packed. Atoms do not field evaporate from the interior of closely packed planes on the surface, but rather, they will evaporate from the edges of a plane on the curved surface. This means that facets are formed where closely packed planes exist (normal to low index orientations), as shown in Fig. 15.22a-cc. Facets on the evaporating surface cause distortions in the reconstructed image when a spherical back projection is used since these regions deviate from spherical locally. Indeed, Stephenson et al [15.109] have shown that if these regions of distortion are removed from the data, an SDM of the remaining atoms shows a much tighter distribution, i. e., higher spatial resolution. In these reconstructions, the number density of atoms in the center of a faceted region will be lower than the surrounding region. This type of image distortion is referred to as monophase distortion to distinguish it from polyphase distortions described below. Monophase distortions can be readily seen in evaporation histograms, that is, an integration of ion hits on the detector (Fig. 15.22a-cc). The locations of facets at low index poles and along zone lines is readily evident as the dark spots and lines, respectively.

Such distortions in the reconstructed image also occur when deviations of the evaporating surface from spherical are caused by the presence of multiple phases at the surface. This polyphase distortion can be even more severe than the monophase distortions. The origin of this distortion is illustrated schematically in Fig. 15.23a-d. When the endcap is spherical, as in Fig. 15.22a-ca, the standard spherical reconstruction algorithm [15.79, 15.80] does an excellent job. With increasing difference in the evaporation field, \(E_{\text{ev}}\), between the phases, distortions in the image increase in magnitude. Instead of a relatively smoothly varying atom number density across the reconstructed image, these distortions lead to local density variations. There is a progression in severity of the distortion from none for a spherical endcap, as in Fig. 15.22a-ca, to moderate as illustrated in Fig. 15.23a-da, to severe as illustrated in Fig. 15.23a-db. An extreme example of distortion is shown in Fig. 15.23a-dc [15.96] where the evaporation fields of Si and \(\mathrm{SiO_{2}}\) are sufficiently different that a concave surface is formed on the evaporating apex. So long as the distortions are not too severe, the principal consequence is the local density variation. The relative positions of all atoms must be maintained, even if their interatomic spacings are not correct. Once the projection distortion reaches a critical point, however, ions cross paths and information is lost. There is no known fix for ion crossing, and it represents a distortion that may not be fixable.

Ion Identification Ambiguity

Though image distortion is paramount for some applications , composition accuracy is another challenge for some materials. It might seem that composition determination in atom probes could not be simpler: just count the atoms. There are, however, several ways that incorrect composition determinations may be made. In time-of-flight spectrometry, there can be more than one species that corresponds to a given flight time (mass-to-charge state ratio). For example, if a calibrated time of flight indicates \(m/n={\mathrm{14}}\,{\mathrm{Da}}\), the species could be \(\mathrm{{}^{14}N^{+}}\), \(\mathrm{{}^{28}Si^{2+}}\), or \(\mathrm{{}^{56}Fe^{4+}}\). If we are running silicon nitride, we may conclude that it is not likely to be \(\mathrm{{}^{56}Fe}\). This can also be checked for other isotopes since if there is \(\mathrm{{}^{56}Fe}\) present, there should be a peak corresponding to \(\mathrm{{}^{57}Fe}\) as well. However, the ambiguity between N and Si is not readily resolved with just time-of-flight information. A similar ambiguity exists for the species \(\mathrm{{}^{16}O^{+}}\) and \(\mathrm{{}^{16}O_{2}^{2+}}\). In this case, there is not a strong second isotope available that could be used to sort out the ambiguity. The problem is that we do not know in such a case whether to count hits in the \(m/n={\mathrm{16}}\,{\mathrm{Da}}\) peak as one oxygen or two. A potential solution for this problem in time-of-flight spectrometry was identified by researchers working on superconducting detectors [15.110], and was discussed as a possible solution for atom probes by Kelly [15.111]. Any detector that can record information relating to the kinetic energy of an ion in addition to its flight time could resolve this ambiguity. Detectors which provide kinetic energy information based on superconductivity [15.112] are being developed.

Another source of composition skewing error is inadequate multihit detection. The delay-line detectors in widespread use today have a finite pulse-pair time resolution. Two hits at the same point that are separated by less than the pulse-pair time resolution will be recorded as one hit. Similarly, since position along the delay line corresponds to a propagation time, two hits at the same time separated by a distance that is less than the pulse-pair time (distance) resolution, will also be recorded as one hit. For most materials, the chance of simultaneous field evaporation events is small enough to neglect. But in a few cases, the limitations of multihit detection are problematic. For boron dopants in silicon, the boron atoms tend to migrate on the surface and form two-atom clusters. When one boron atom in a cluster evaporates, the second is suddenly left exposed on the surface and it too evaporates. This effect is only large enough to become significant when boron concentrations approach one atomic percent, but it can reduce the measured boron concentration by a factor of \(\mathrm{2}\) in such cases [15.72, 15.74]. Similar problems can occur with carbon atoms in steels [15.73].

There are also other potential sources of lost atoms. If they affect all atom types equally, then there is no impact on composition determination. One such effect is the detection efficiency of MCP/delay-line detectors. MCPs have a detection efficiency of \(55{-}80\%\) typically [15.113] due to the finite open area at the entrance of the MCP. In the range of ion masses and energies employed in atom-probe tomography, there is no measurable bias in detection efficiency with ion mass up to masses of about \({\mathrm{500}}\,{\mathrm{Da}}\). In the case of a reflectron instrument, there will also be an entrance mesh through which the ions pass twice. This mesh is usually better than \({\mathrm{80}}\%\) open and does not introduce a bias with ion mass.

Another common observation has been incorrect composition determinations in materials where the stoichiometry is well known such as certain oxides and compound semiconductors. A common explanation has been that there must have been atoms that evaporated outside of the pulse event and therefore contribute to the background between peaks and are not counted. Gault et al [15.114] have recently analyzed this situation in detail and concluded that this effect is likely caused by molecular ions which evaporate and then dissociate during flight. If the molecular ion has a charge state of one, then only one of the dissociation fragments will remain charged after dissociation. If the dissociation occurs early while the ion is still being accelerated, then the flight time of the remaining ion will be shorter. and the neutral(s) may or may not have enough energy to make it to the detector in time to be counted. Saxey [15.115] analyzed this scenario of ion fragmentation and showed that the dynamics can be analyzed to recover the fragmented pair identity and ion lifetime in many cases. This type of analysis should become a standard feature in atom probe analysis algorithms.

As noted below in Sect. 15.6, it is often very desirable to augment atom probe information with structural and analytical information. In this regard, one should remember that atom-probe tomography is a compositional mapping technique, and adjuncts such as (S)TEM images, diffraction information, and especially chemical information from electron energy-loss spectroscopy are a welcome addition.

15.3.2 Strengths of APT

Many of the strengths of APT shall be on display in Sect. 15.5. However, it is worth emphasizing several key points in this section. Firstly, the data in APT are inherently three-dimensional and discrete. It doesn't get more discrete than atomic: the data are determined one atom at a time. The limitations noted above notwithstanding, in the general case, all atoms are detected with equal efficiency and thus composition determinations are straightforward. There is a very low noise floor in APT. It is common for peak-to-background signals to exceed \(\mathrm{10^{5}}\). This makes it possible to achieve very high analytical sensitivity on the order of one atomic part per million (appm ). This sensitivity is not achieved in all materials for all elements, but there are many cases where it is achieved. The best scenario is for a single-isotope element (the whole signal is in one peak) to be found at low concentration in a material where there are no peak interferences or ambiguities. This high analytical sensitivity is coupled with a very high spatial resolution on the order of \({\mathrm{200}}\,{\mathrm{pm}}\) or better. It is this combination of high analytical sensitivity and high spatial resolution that is unique in analytical instrumentation and is the most important point to remember. The common map of analytical instrumentation space made popular by EAG, Inc. illustrates this point well (Fig. 15.25). Atom-probe tomography occupies the high sensitivity, high spatial resolution region of this plot.

Fig. 15.25

Map of analytical instrumentation space (after EAG chart of a similar nature). Note that the lower left highlighted region is unphysical since, for example, it does not make sense to describe part per trillion sensitivity for a collection of a million atoms

The detection efficiency of atom-probe tomography was noted in the discussion on limitations of the technique. However, it is also a strength. Though we do not yet have \({\mathrm{100}}\%\) detection efficiency, and we desire it, actual detection efficiencies today of \(38{-}80\%\) are very high by most analytical technique standards.

It is also worth noting that the time to knowledge of about one day is comparable to most advanced microscopies. A high level of automation has been applied to specimen preparation and analysis for (S)TEM in the past few years, and the time to knowledge has been reduced to a few hours. It is likewise possible to imagine similar efforts applied to atom-probe tomography to reduce the time to knowledge to comparable time.

15.4 Specimen Preparation

In the first 30 years of the atom probe , field pulsing was the only pulsing method that was widely practiced. Since the specimen must have relatively high electrical conductivity for field pulsing to work, atom probe analysis was almost exclusively performed on metals during this time. Though multiple possibilities exist for making sharp needles from metals, electropolishing methods are and were the dominant method used. Melmed [15.116] reviewed the state of specimen preparation for making sharp needles, which in 1991 did not include much ion milling. Overviews of electrochemical polishing methods are also available in the several textbooks on atom-probe tomography [15.117, 15.16, 15.40, 15.48, 15.80].

15.4.1 Electropolishing

When electrochemical means are appropriate for a given material and application type, it can produce specimens of high quality in a brief time with low expense. Figure 15.26a,b illustrates the basic concept. Starting with a wire specimen or square-section cut rod of less than \({\mathrm{1}}\,{\mathrm{mm}}\) diameter, a ring-shaped cathode is located around the region of interest. and when this geometry is immersed in an electrolyte, the specimen electropolishes near the loop to form a neck. In the limit where this neck electropolishes down to nothing, two sharp needles are made. The method in Fig. 15.26a,b may also be terminated prior to separation of the two pieces, and a final polish may be applied without a ring as shown in Fig. 15.27a,b. The loop method shown in Fig. 15.28 is popular because it is possible to control where the material removal occurs by moving the specimen relative to the loop. These loops are typically \({\mathrm{3}}\,{\mathrm{mm}}\) in diameter, which means they hold about one drop of electrolyte. The loop method is useful when more control over the shape and location of the needle apex are needed. Because of its small volume, the drop will become exhausted of electrolyte after a minute or so, and it is necessary to replenish the drop regularly.

Fig. 15.26a,b

Schematic of a typical loop-style electropolishing geometry. The entire apparatus would be immersed in an electrochemical solution: (a) initial setup, (b) final geometry just prior to separation of two needle-shaped specimens

Fig. 15.27a,b

Once a wire has been necked, it is possible to create the final tip by uniform electropolishing of the entire remaining wire. Two common approaches include (a) full immersion of the necked wire in an electrolyte and (b) localization of the polishing action in a layer of electrolyte floating on a dense, inert liquid. After [15.116]

Fig. 15.28

Schematic of a typical loop-style electropolishing geometry. The specimen would be moved horizontally relative to the Pt wire loop/electrolyte which serves to control the location of the material removal

15.4.2 Focused Ion Beam Milling

One of the most significant changes in atom-probe tomography in the past two decades is the near full switch to focused ion beam milling for preparation of specimens. The electrochemical method works well when the specific location of the analyzed region is not important. However, preparation of specimens from specific locations, like a grain boundary for example, is difficult even with the loop method. The use of modern FIB instruments to perform lift-out specimen preparation has revolutionized the atom probe (see a brief review in [15.68]). If a feature of interest is visible in the FIB instrument, it is possible to locate a feature within the analyzed volume of an atom probe to within \({\mathrm{10}}\,{\mathrm{nm}}\) nowadays, so site-specific analyses of materials such as single transistors can be readily accomplished.

The earliest efforts at using a focused ion beam (FIB) to make atom probe specimens dates to work by Waugh et al [15.118] and Alexander et al [15.119]. Though the early instrument was limited in its performance, these researchers recognized the many advantages of sculpting material and being able to select a specific location from a specimen and prepare it for APT analysis. There were several early methods of using FIB [15.120, 15.121], but eventually the lift-out method that was developed for TEM specimen preparation became a standard approach [15.122, 15.123, 15.124, 15.125, 15.126]. Today, in the author's estimation, well over \({\mathrm{90}}\%\) of all atom probe specimens are made by a FIB. Coupons may be lifted out from a surface and mounted on either a needle or a microtip. Microtip arrays were developed by Imago Scientific Instruments for use with the LEAP instrument (Fig. 15.20a-d). These arrays were made in two types: presharpened, as in Fig. 15.20a-dc, and flat top, as in Fig. 15.20a-dd. They are fabricated from heavily doped silicon wafers by microelectromechanical system ( ) techniques. The presharpened microtips ( ) may be directly inserted into a LEAP as they have a radius of about \({\mathrm{75}}\,{\mathrm{nm}}\) at the apex. PSMs may be run simply for an easy silicon specimen, but are usually used for thin-film studies, where the films can be deposited directly on the coupon and will coat the apex region. However, the clear majority of microtip arrays sold are flat-top arrays. These flats are about \({\mathrm{2}}\,{\mathrm{\upmu{}m}}\) in diameter at the apex and are used as a receptacle for lifted-out material in the FIB.

The lift-out method is illustrated in Fig. 15.29a-f following [15.125]. A thin layer of Pt deposit is applied in the FIB (Fig. 15.29a-fa). Two trenches are then cut on either side of the Pt deposit, and one end of the resultant beam is cut free (Fig. 15.29a-fb). These trenches are dug at a \(22^{\circ}\) angle to the surface such that they intersect the subsurface to create a wedge shape (Fig. 15.29a-ff). A micromanipulator is attached to the free end of the beam by a Pt deposit, and the tethered end is then cut free (Fig. 15.29a-fc). The micromanipulator is used to position the liberated coupon above a microtip (or needle) as shown in top view (Fig. 15.29a-fd) and side view (Fig. 15.29a-fe). A Pt deposit is used to bond the coupon to the microtip, and it is cut free (Fig. 15.29a-fe), leaving an extracted piece mounted on a microtip (Fig. 15.29a-ff).

Fig. 15.29a-f

Illustration of the lift-out method of FIB preparation of microtip specimens for LEAP. See text for details. From [15.127] Copyright 2011 World Scientific

The extracted piece, as shown in Fig. 15.30a-fa, must be sharpened for atom probe analysis. The specimen is rotated to bring its long axis in line with the ion column axis and annular scanning of the ion beam is initiated (Fig. 15.30a-fb). The annular milling geometry may be changed in steps or continuously to produce a smaller inner radius of the pattern with advancing milling (Fig. 15.30a-fc–e). If the feature of interest is visible in the image (secondary electron, backscattered, …), then it may be positioned relative to the annular milling pattern, e. g., in Fig. 15.30a-fd or Fig. 15.30a-fe.

Fig. 15.30a-f

Illustration of the sharpening method of FIB preparation of microtip specimens for LEAP. See text for details. From [15.127] Copyright 2011 World Scientific

Usually, the annular milling is stopped when the operator determines that about \({\mathrm{50}}\,{\mathrm{nm}}\) of material removal remains. Up to this point, fast milling is desired and usually a \({\mathrm{30}}\,{\mathrm{kV}}\) beam is used. The final \({\mathrm{50}}\,{\mathrm{nm}}\), however, is usually removed at a low accelerating potential like 5 or \({\mathrm{2}}\,{\mathrm{kV}}\) in order to remove Ga ion implantation and damage [15.125] (Fig. 15.31a,b). This last step does not require a focused ion beam, so it can be done by simply changing the accelerating potential without refocusing, and then scanning over the area for about one minute. The result is shown in Fig. 15.30a-ff, which is ready for analysis.

Fig. 15.31a,b

Removal of \(\text{Ga}^{+}\) damage in FIB. (a) Concentration profile of Ga into a silicon specimen after \({\mathrm{30}}\,{\mathrm{kV}}\) milling and \({\mathrm{5}}\,{\mathrm{kV}}\) milling. (b) Mass spectrum of Ga where the \(\text{Ga}^{+}\) signal decreases with accelerating potential and is not detectable at \({\mathrm{2}}\,{\mathrm{kV}}\). After \({\mathrm{2}}\,{\mathrm{kV}}\) milling, there is no detectable level of Ga in the specimen in the first one million ions. Reprinted from [15.125], with permission from Elsevier

Many variants of this basic approach have been developed as needed. Admittedly, this technique requires an expensive FIB instrument, but the flexibility and precision achieved makes it possible to create specimens that either a) formerly took several days with other methods if they succeeded at all, or b) are impossible by other means. Certainly, the cost of the added instrumentation is justified in many applications, especially since FIB instruments have become standard in analytical characterization laboratories.

15.5 Applications

A selection of several applications is reviewed here to provide a survey of what can be done with APT. The applications are chosen to represent different analysis types or ways that APT has delivered value to a study.

One theme that is clear is that atom probe and (S)TEM are often both utilized in materials studies. This fact can be traced all the way back to the earliest days of atom probe. APT specimens are well suited for study by (S)TEM: they are electron-transparent at the apex region. But the attraction goes well beyond this fact. The two techniques are strongly complementary, that is, the strengths of one technique overcome the limitations of the other and vice versa. For example, APT remains challenged to deliver accurate (spatially calibrated) length scales, which is one of (S)TEM's strengths. (S)TEM is challenged to deliver high sensitivity at the smallest length scales, which is APT’s strength. In Sect. 15.6, the prospects for a combined instrument are explored. Until that is realized, correlative methods have been utilized, as will be evident in the examples below.

15.5.1 Metals

Metals were the first materials studied with APT. Indeed, metals were the first materials to be engineered at the atomic scale. They remain among the most fascinating of materials. There is a rich variety of microstructures, and atom probe delivers very high-quality information.

Linear Complexions in Steel

Defects in materials control their properties even though they occur on the finest length scales. An unusual and newly discovered defect, a linear complexion, has been observed and characterized by correlative (S)TEM and APT by Kuzmina et al [15.128] (Fig. 15.32a-e). This correlative study demonstrates a fine synergy between the two techniques.

Fig. 15.32a-e

Fe-\({\mathrm{9}}\,{\mathrm{at.\%}}\) Mn solid solution, \({\mathrm{50}}\%\) cold-rolled and annealed at \({\mathrm{450}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\) for \({\mathrm{6}}\,{\mathrm{h}}\) to trigger Mn segregation. (a) Bright-field STEM image. (b) Correlative atom-probe tomography results of the same tip shown in (a) using \({\mathrm{12.5}}\,{\mathrm{at.\%}}\) Mn isoconcentration surfaces (\({\mathrm{12.5}}\,{\mathrm{at.\%}}\) Mn was chosen as a threshold value to highlight Mn-enriched regions). The blue arrows mark grain boundaries and dislocation lines that are visible in both the STEM micrograph and the atom-probe tomography map. Not all dislocations visible in STEM are also visible in the atom probe data and vice versa (red arrows). (c) Overlay of (a,b). (d) Magnification of two subregions taken from (b). (e) One-dimensional ( ) compositional profiles along 1 (perpendicular to dislocation line) and 2 (along dislocation line). From [15.128]. Reprinted with permission from AAAS

An array of dislocations in a bcc (martensitic) Fe-\({\mathrm{9}}\,{\mathrm{at.\%{\,}Mn}}\) steel is observed by diffraction contrast in TEM (Fig. 15.32a-ea). Through compositional mapping and proximity histograms [15.130] for \({\mathrm{12}}\,{\mathrm{at.\%{\,}Mn}}\) isoconcentration surfaces [15.80] in APT, it was shown that some of the dislocations exhibit the presence of an atmosphere (Fig. 15.32a-eb,d). The nominal composition within the isoconcentration surfaces is about \({\mathrm{25}}\,{\mathrm{at.\%{\,}Mn}}\), which is normally an fcc (austenitic) composition. Using dark-field imaging in TEM, they could show that the high Mn volumes in these linear features obeyed a Kurdjumov–Sachs relationship with the parent bcc structure. Furthermore, it is only the edge dislocation segments that have the atmospheres. These results prove that the edge dislocations, which contain high-Mn atmospheres, have a strain-stabilized fcc structure, consistent with the austenitic phase. Compositionally stabilized phases at a surface have previously been observed and were called complexions [15.131]. These compositionally stabilized linear phases were termed linear complexions by the authors. Furthermore, periodic Mn variations along the dislocation cores were observed (Fig. 15.32a-ee). These periodicities are explained as Rayleigh instabilities which are driven by minimization of the interfacial area. Clearly, both STEM and APT brought unique information to the study and a much greater understanding of the microstructure resulted.

Electron Diffraction and APT

Electron diffraction is a key adjunct to atom-probe tomography. The precision and surety of identification of crystal structure, orientation, and strain complement the modest structural capabilities of atom-probe tomography. Prior to collecting atom probe data, it can be an essential complement to specimen preparation techniques. Often, segregation is observed at an internal surface in an APT image. In such cases, it is tempting to describe the surface as a grain boundary, but there are two problems with this. One, there is usually no direct proof that the surface is a grain boundary, and two, the character of the boundary is unknown. Electron diffraction during specimen preparation or during the analysis (in a combined APT/(S)TEM) would readily answer these questions. Rice et al [15.129] used transmission Kikuchi electron diffraction recorded in a FIB with an electron backscatter diffraction camera to locate grain boundaries in an Inconel 600 alloy (Fig. 15.33a-d). The yellow dashed line demarcates a boundary between two grains in Fig. 15.33a-da. Additional milling is used to erode the tip, as shown in Fig. 15.33a-db, to the point that the grain boundary is within reach of APT analysis after the final milling step at \({\mathrm{2}}\,{\mathrm{kV}}\) is used to achieve the specimen shown in Fig. 15.33a-dc. This low-kilovoltage final milling removes Ga implantation damage, which improves the quality of the Kikuchi patterns. Because of the preparation, atom maps shown in Fig. 15.33a-dd are obtained at a grain boundary of known character. Segregation of B to this grain boundary is especially evident.

Fig. 15.33a-d

Analysis of an Inconel 600 alloy. (ac) Transmission Kikuchi patterns during the milling process taken at \({\mathrm{30}}\,{\mathrm{kV}}\) used in preparation of atom probe specimens of a grain boundary. (c) Final milling was performed at \({\mathrm{2}}\,{\mathrm{kV}}\) to remove damage. (d) Atom maps of Ni, B, and C showing segregation at the grain boundary identified by the dashed line. The misorientation of the two grains is \(50^{\circ}\). From [15.129], reproduced with permission

Atom-Probe Crystallography

Gault et al [15.132] have reviewed the advanced use of crystallographic information from APT, mostly derived from spatial distribution maps. Though it is not yet a strength of APT, it is possible to determine such information as the orientation and crystal structure of grains a few nanometers in size and in proximity to each other (Fig. 15.34). They show how this capability can: reveal atomic planes in ceramics and semiconductors in addition to metals; be used to calibrate reconstructions; investigate short-range ordering; enable characterization of precipitates and ordered phases on a nanoscale; enable characterization of crystalline defects such as dislocations and dislocation loops; and provide orientation mapping and grain boundary misorientation information. Figure 15.34 illustrates this last point. The central figure is an APT tomograph of a nanocrystalline aluminum specimen. The orientation of each grain in the tomography has been determined, and the grains are colored per the inverse pole figure shown. Ga is observed to be segregated to the grain boundary. This 3-D orientation map is like those from serial-section FIB orientation maps, but they are on a much finer scale. It is possible to determine the disorientation of any pair of grain boundaries and correlate segregation levels with grain boundary curvature, roughness, and disorientation for a robust characterization at the nanometer scale.

Fig. 15.34

Atom probe orientation mapping in nanocrystalline aluminum. Ga segregation at the grain boundary is evident. The zoomed-in image on the left of the reconstructed volume shows that the imaged atomic planes extend up to the grain boundary, and the graph on the right is a proximity histogram highlighting the extent of the segregation at the grain boundary. The grains in the central image are colored according to their orientation, as indicated by the inverse pole figure. Reprinted from [15.132], with permission from Elsevier

15.5.2 Ceramics

Analysis of ceramic materials did not become routine until the advent of commercial laser-pulsed atom probes in about 2006. There was concern in the community that ceramic materials could never be analyzed in a laser-pulsed atom probe, for two main reasons: a) the applied electric field would penetrate the dielectric material and there would not be a high field at the surface to effect field evaporation, and b) even if the electric field was high enough at the apex, typical laser photon energies of \({\mathrm{3}}\,{\mathrm{eV}}\) or less would not have enough energy to be absorbed in a material like aluminum oxide, which has a band gap of \({\mathrm{8}}\,{\mathrm{eV}}\) or more. Fortunately, neither of these issues, which are extrapolations from bulk material behavior, directly applies to atom probe conditions as explored by Kelly et al [15.63] and Vella [15.62]. Briefly, the reason these materials may be analyzed in atom probe is that some combination of surface band bending under high electric field and/or surface defect states makes it possible for charge to accumulate on the surface and absorb photons of lower energy.

Grain Boundary Segregation in Nd-doped Ceria

Many studies have now shown that ceramic materials can be run successfully and produce excellent results. Diercks et al [15.133] studied grain boundary segregation of multiple species in a \({\mathrm{10}}\%\) Nd-doped ceria (Fig. 15.35a,b). In Fig. 15.35a,bb, quantitative 3-D maps of the key atomic species in this material show segregation of Nd, Al, and Si coupled with O depletion at the grain boundary. This information was used to support electrostatic modeling of these structures and correlate with macroscopic electrochemical impedance spectroscopy measurements to yield 3-D potentials at the grain boundaries. When the Nd concentration was \({\mathrm{30}}\%\), local gaps in the 3-D potentials suggest conduction pathways through the potential barrier at the grain boundary.

Fig. 15.35a,b

Atom probe data from a grain boundary in Nd-doped ceria. The boxes in (b) represent local composition in \(\mathrm{at.\%}\) at the location shown in (a). The grain boundary passes through the center of the box and is most evident in the Nd excess and O deficiency. Reproduced from [15.133], with permission of The Royal Society of Chemistry

Isotopic Mapping in Zircons

In some studies, the ability of atom-probe tomography to map isotopes is essential to the work. Secondary ion mass spectroscopy ( ) is often used for isotopic mapping in geological materials on the \(\mathrm{\upmu{}m}\) scale and larger. Zirconium silicate (zircon) is a hard, high-melting-temperature mineral that survives geologic processes (grinding, heating, chemical attack) better than most other minerals. It is often found as a small detrital component in rocks. It is well known that when zircons crystallize from the melt, large-impurity dopant atoms like Pb are rejected at the growing crystal/liquid interface, while smaller-impurity atoms of elements such as Y and U are incorporated. This fact is utilized in a method of measuring the time since crystallization of the zircon. Essentially, \(\mathrm{{}^{206}Pb}\) is a daughter product of \(\mathrm{{}^{238}U}\) with a known half-life of \(\mathrm{4.5}\) billion years, so any \(\mathrm{{}^{206}Pb}\) found must be from radioactive decay of the \(\mathrm{{}^{238}U}\), and the ratio of these two isotopes gives the time since crystallization. In fact, the \(\mathrm{{}^{207}Pb/{}^{235}U}\) ratio also gives a time, and thus there are two clocks in zircons that can be checked against each other. In 2001, Wilde et al [15.134] used this zircon geochronology to date a zircon from western Australia as \(\mathrm{4.4}\) billion years old (\({\mathrm{4.4}}\,{\mathrm{Ga}}\)). This result had profound implications for the early earth and solar system, since it indicated that the earth had components of a solid crust a mere \({\mathrm{0.16}}\,{\mathrm{Ga}}\) after the solar system was formed (\({\mathrm{4.56}}\,{\mathrm{Ga}}\)). Since the analysis was limited by SIMS to greater than \({\mathrm{1}}\,{\mathrm{\upmu{}m}}\) lateral resolution, there were concerns that unseen microstructural features such as Pb diffusion, Pb inclusions, or infilled cracks could skew the result. Given the import of the implications, the door remained open for questions of the validity of the result. Valley et al [15.135] used atom-probe tomography to experimentally reexamine the very same zircon (Fig. 15.36a-c). One run shown in Fig. 15.36a-ca was over a \(\mathrm{\upmu{}m}\) in depth and contained \(\mathrm{400}\) million atoms. It showed that there were no large Pb reservoirs that might skew the results. The overall Pb/U isotope ratios gave the same age as the SIMS results had. There was further evidence of Pd diffusion on a length scale of \({\mathrm{50}}\,{\mathrm{nm}}\) to Y-rich clusters that were thought to have formed during a known heating event at \({\mathrm{3.4}}\,{\mathrm{Ga}}\). The Pb content of the surrounding matrix dated at \({\mathrm{3.4}}\,{\mathrm{Ga}}\) which indicated that all the Pb had diffused to the Y-rich clusters during the heating event, and the remaining U in the surrounding matrix then decayed for the next \(\mathrm{3.4}\) billion years; i. e., the Pb was immobile except for the known heating event. This study provided the conclusive evidence needed to close the door on the prospect of artifacts altering the dating of these zircons and supported the notion that a radical rethinking of the early earth geologic history was required.

Fig. 15.36a-c

Atom-probe tomography data from a \({\mathrm{4.4}}\,{\mathrm{Ga}}\) zircon. The Pb and Y atom maps in (a) show clear clustering of Y and detectable clustering of Pb. The regions outlined in boxes are enlarged in (b). The cluster outlined with a box in (b) is shown in (c) with the \(\mathrm{{}^{206}Pb}\) and \(\mathrm{{}^{207}Pb}\) isotopes displayed separately. From [15.135]

15.5.3 Semiconductors

Semiconductor materials have represented a major application space for APT in the past decade. There have been several recent reviews dedicated to this topic [15.126, 15.136, 15.137, 15.138, 15.139]. Overall, the application of atom-probe tomography to semiconductor materials has been very fruitful. However, there are difficulties that arise with each of the major material types: Complementary metal–oxide–semiconductor ( ) structures and compound semiconductors. The following applications highlight these challenges, which will hopefully alert the reader to the appropriate considerations. By understanding these challenges, we may identify strategies to reduce or eliminate the problems they produce.

CMOS Structures

Given the size of CMOS structures today and projected into the future, there is great interest is seeing every atom in three dimensions. APT is uniquely capable of satisfying this need, but there are two principal challenges in this pursuit: a) specimen fracture during a run is usually high (can be \(> {\mathrm{75}}\%\)) due to the multiplicity of disparate phases in a typical CMOS transistor, and b) reconstructions of the polyphase data sets usually contain obvious distortions which result from differences in evaporation fields between the phases. One strategy has been to deprocess a structure to remove at least the field dielectric (usually silicon dioxide), and then replace it with conformal polysilicon so that specimens run well and the distortions are minimized. Inoue et al [15.140, 15.141, 15.142] have on multiple occasions published fine examples of APT data from CMOS structures. In Inoue et al [15.142], the authors examined two different CMOS devices of unknown (to them) structure a priori and obtained APT analysis of both n- (metal–oxide–semiconductor field-effect transistor) and p-MOSFET transistors (Fig. 15.37). They observed differences in the dopant distributions between the two products and between the n-type and p-type transistors. The Ni silicide/polysilicon gate, gate oxide, and channel region were studied in each case. The gate polysilicon in the n-MOSFETs had clearly different dopants between the two products, especially for As and C. As transistor scaling reaches sub-\({\mathrm{10}}\,{\mathrm{nm}}\) lengths, APT may be the only technique that can deliver such quality information on such devices. However, the challenges mentioned above will need to be solved if the technique is to be fully embraced in the semiconductor industry. The specimen failure challenge has been solved by some commercial groups, but the image distortion challenge remains. Section 15.6 discusses approaches to resolving the distortion challenge, and the outlook suggests viable solutions within the next \(\mathrm{5}\) years.

Fig. 15.37

Analysis of two distinct CMOS devices (Products I and II) for dopant distribution and structural content. The TEM images show the n-type and p-type transistors in section with a yellow dashed line depicting the regions from which atom probe data are shown to the right. The atom maps from APT analysis show clear differences in dopant distributions in the gates, especially for the n-MOSFETs. The silicides were found to be \(\mathrm{NiSi_{2}}\) based on atomic composition. From [15.142]. Copyright 2013 The Japan Society of Applied Physics

It is worth noting that time to knowledge is another critical consideration in such work. A one-day or two-day turnaround on specimens is acceptable in a research and development setting, but in commercial manufacturing, if APT is to contribute to design realization and especially yield ramp, the time to knowledge will need to be reduced to \({\mathrm{5}}\,{\mathrm{h}}\). This target is achievable, but will require engineering development.

Compound Semiconductors

There has been much interest in analyses of compound semiconductors by APT. These materials generally run well, but the challenge has been to be confident in the composition determination especially since these materials are usually stoichiometric. Recent work by Rigutti et al [15.143] illustrates the challenge well and offers a potential solution based on correlative information. In their work, the structure consists of 15 repeats of a \({\mathrm{20}}\,{\mathrm{nm}}\)-thick \(\mathrm{Al_{\mathit{y}}Ga_{1-{\mathit{y}}}N}\) barrier layer followed by an \({\mathrm{1}}\,{\mathrm{nm}}\,\mathrm{Al_{\mathit{x}}Ga_{1-{\mathit{x}}}N}/{\mathrm{3}}\,{\mathrm{nm}}\,\text{GaN}/{\mathrm{2}}\,{\mathrm{nm}}\,\mathrm{Al_{\mathit{x}}Ga_{1-{\mathit{x}}}N}\) quantum well sandwich where \(y={\mathrm{0.25}}\) and \(x={\mathrm{0.64}}\). Figure 15.38 shows atom maps of seven of these layers and a mass spectrum for the full data set. Note the presence of some molecular ions in addition to monatomic ions. The layer spacings are well calibrated from TEM and were used to calibrate the spatial dimensions of the APT reconstruction. The correct layer spacing can be achieved in the reconstruction by adjusting the adjustable reconstruction parameters, but this resulted in a derived value of the detection efficiency of \({\mathrm{22}}\%\). The nominal value would be \({\mathrm{60}}\%\) in this instrument. This raised the question, which has been raised by other authors as well, of whether there is a systematic loss of some atoms. The supposed loss mechanisms include field evaporation between pulses (out-of-pulse (OOPs ) events), neutral evaporation of species such as \(\mathrm{N_{2}}\), and field evaporation of molecular ions followed by dissociation. Each of these could result in ions or neutrals landing in the background instead of in peaks. These authors noted that the measured ratio of group III elements to nitrogen in these structures and the aluminum site fraction, \(y\), varied with applied electric field (charge state ratios were used as a proxy for applied electric field) (Fig. 15.39). It is clear for the regions of interest ( A and ROI B) in these data that the atomic fractions for \(\text{Al}+\text{Ga}\) and N in the barrier layers approached the expected \({\mathrm{50}}\%\) at relatively low applied electric fields (\(\mathrm{Ga^{2+}}/\mathrm{Ga^{+}}\leq{\mathrm{0.05}}\)). The aluminum site fraction also varied markedly with applied electric field, as shown in Fig. 15.39c, and only approached the nominal value at the lowest fields observed. Through their careful observation of regular trends in the data, the authors developed a statistical correction procedure that correlated photoluminescence data with APT data to calibrate the actual composition and site occupancy. The exact mechanism by which the composition measurements were skewed was not established.

Fig. 15.38

(a) SEM image of the analyzed field-emission tip containing the GaN/AlGaN MQW system; the sketch on the top right-hand side corresponds to the volume analyzed by APT. (b) APT reconstructed volume, showing \({\mathrm{100}}\%\) of Al\({}^{1+}\) (green) and Al\({}^{2+}\) (red) ions and the separately analyzed regions of interest (s); (c) as in (b), but with \({\mathrm{20}}\%\) of Ga\({}^{1+}\) (magenta) and \({\mathrm{100}}\%\) Ga\({}^{2+}\) (blue) ions. (d) Mass/charge spectrum of the whole data set, reporting the labels of the main peaks; the color code of the peaks corresponds to that of parts (b) and (c). Reprinted from [15.143], with the permission of AIP Publishing

Fig. 15.39

(a) and (b) Atomic fraction of Ga (black squares), Al (blue circles) \(\text{Al}+\text{Ga}\) (violet triangles), and N (red triangles) as a function of the \(\mathrm{Ga^{2+}}\)/\(\mathrm{Ga^{+}}\) charge state ratio extracted from the detector space statistics of ROI A (a) and ROI B (b), respectively. (c) The Al site fraction, \(y\), plotted versus the \(\mathrm{Ga^{2+}}\)/\(\mathrm{Ga^{+}}\) charge state ratio—both quantities are issued from the detector space statistics of ROI A (black squares, high field) and ROI B (brown triangles, low field); the red solid line is a guide for the eye. Reprinted from [15.143], with the permission of AIP Publishing

Gault et al [15.114] have questioned the supposition that neutral atom or neutral molecule evaporation may occur in such experiments. They cite the fact that the binding energy of atoms on a surface even under the extreme electric fields is such that neutral evaporation cannot happen in a detectable manner. Rather, they conclude that molecular ion field evaporation followed by dissociation is a viable and experimentally supported explanation. We know that molecular ions dissociate, and the fragments can be detected in the atom probe. Based on the pioneering work of Saxey [15.115] on analysis of the dissociation products from molecular ions in atom probe (Fig. 15.40a,b), these evaporants may be identified. Figure 15.40a,ba is a histogram of the correlations for double-hit events on the detector per pulse cycle. Each axis is the mass-to-charge state ratio, \({m}/{n}\), of one of the ions of the pair. The features of this figure may be understood as follows:
  1. 1.

    A single point is plotted in the histogram for each ion pair and the figure is mirrored about its diagonal.

     
  2. 2.

    Vertical and horizontal lines are caused by an ion pair where one ion evaporates during the pulse and the second ion evaporates some \(\Updelta t\) later.

     
  3. 3.

    Diagonal lines are caused by an ion pair that evaporates at the same time but some \(\Updelta t\) after the pulse.

     
  4. 4.

    Extended arcs are caused by dissociation of molecular ions where the dissociation event leaves each ion with one or more charges and occurs early enough in the flight that each ion receives additional acceleration. One such event type is labeled in red in Fig. 15.40a,ba.

     
  5. 5.
    There are multiple potential cases for dissociations that produce some neutrals:
    1. a)

      One dissociation product is charged, and the other is neutral. This pair may show up on this histogram if the neutral can incite a detection event. If the dissociation event occurs later in the flight, the neutral may hit the detector. If the neutral has enough energy (\(\geq{\mathrm{2}}\,{\mathrm{keV}}\)) to excite the microchannel plates, it may be detected. If the dissociation event occurs early, the neutral will continue on a tangential path that may not intercept the detector and will be lost.

       
    2. b)

      At least two dissociation products are charged and at least one is neutral. The dissociation product pairs should appear on the dissociation histogram, but the neutral may not appear. The track highlighted by the thin gray line in Fig. 15.40a,bb is an example of \(\mathrm{GaN_{3}^{2+}}\) dissociating into \(\mathrm{Ga^{+}}+\mathrm{N^{+}}+\mathrm{N_{2}}\).

       
    3. c)

      If a neutral is detected, it may appear correlated with any of the ions in the dissociation. In 5b above, there would be three possible correlated events: \(\mathrm{Ga^{+}}\) with \(\mathrm{N^{+}}\), \(\mathrm{N^{+}}\) with \(\mathrm{N_{2}}\), and \(\mathrm{N_{2}}\) with \(\mathrm{Ga^{+}}\).

       
     
The good news is that this dissociation histogram analysis can be used to resolve the identity of species that would otherwise be lost to analysis. We also learn details of the evaporation process from such analyses that may help us devise strategies for minimizing the effect or design detectors to capture the missing information. Note that these correlation histograms are not available on instruments with reflectrons, since neutrals would never hit the detector and the reflectron compensates for the energy spreads.
Fig. 15.40a,b

Correlation histograms for GaN from [15.114], published under CC-BY 3.0 license. (a) is a section of the histogram which highlights a dissociation into two ions. (b) shows a close-up of the square box in (a), which shows a trace from a dissociation event that includes a neutral that is not detected

Based on this thinking, the reason for missing nitrogen in GaN may be loss of neutrals from molecular ions: 5b above. Strategies for dealing with this issue could include careful use of dissociation histogram analysis to correctly identify, to the greatest extent possible, better detectors that can detect ions and neutrals even at low (\(<{\mathrm{2}}\,{\mathrm{keV}}\)) kinetic energy, and detectors with \({\mathrm{100}}\%\) detection efficiency which would minimize lost multihit events and identify more multihit pairs for such analysis. A brief discussion of new detector concepts that may realize these improvements is provided below in Sect. 15.6.3.

15.5.4 Organics

For as long as there have been atom probers, there has been interest in applying the technique to organic and biological materials. As early as 1950, Müller [15.144, 15.145, 15.146] made attempts to deposit organic molecules on field electron emission needles. Panitz and Giaever [15.147] succeeded in depositing ferritin molecules on field emission tips, and Panitz [15.148] developed a field ion tomography technique to image them. As APT came along and matured, there was renewed interest in this challenge. Kelly et al [15.149] reviewed much of the work of this nature. What has been missing is the infrastructure needed to prepare and introduce into the atom probe, frozen specimens of soft biological tissue that are appropriate for analysis. If one studies the literature, you will find that all of the organic analyses have been performed on specimens that can be prepared at room temperature: hard biological materials [15.150, 15.151, 15.152]; dried tissue [15.153]; polymers [15.154, 15.155]; or chemically stabilized biomolecules [15.156].

This work was important and illuminating, but there was never any doubt that the holy grail has always been the APT analysis of soft biological tissue. Given the routine practice of cryogenic transmission electron microscopy of soft biological tissue, it was obvious what infrastructure was needed. The specimen stage of an atom probe was at cryogenic temperatures anyway, but cryo-transport from the airlock to the stage was needed. This was completed around 2006 for a LEAP by Prosa and Kelly [15.157], which made it possible for others to focus on the rest of the infrastructure. A full set of cryo-preparation tools such as plunge freezing, a cryo-stage for a FIB, a cryo-micromanipulator, and cryo-transport from FIB to LEAP was required. Efforts of this nature have been pursued by Gerstl and Wepf at ETH in Zurich, by Marquis at the University of Michigan, by Perea at Pacific Northwest National Laboratory, and by Gault and Raabe at the Max-Planck-Institut für Eisenforschung in Düsseldorf. These efforts are aimed at a full cryo-preparation process like what has been done successfully for cryo-TEM. This application space for APT is at an early stage, but the requisite hardware is finally becoming commercially available which will allow researchers to focus on making the application work and understanding the results. The next decade should be an exciting one for biological analysis in the atom probe.

15.6 Developments in Atom-Probe Tomography

The three most crucial factors governing success in APT are yield, reconstruction, and detectors. It is constructive to consider where the field stands on each topic.

15.6.1 Yield

If specimens do not run well and produce sufficient quality and quantity of data, then nothing else matters. It is generally the case that when an operator first tries analysis on a material that has never been studied before, there is a learning curve. What is the right specimen geometry? Are there any weak links like weak interfaces in the material? Can we realize site-specific specimen preparation as needed? What is the right laser pulsing or voltage pulsing regimen? And so on. Most monolithic materials will run well with little experimentation. Polyphase materials where there are large interfaces between dissimilar materials are often problematic. For example, we have found that in studying the interface between polymer films on inorganic substrates, it is very difficult to obtain good data, because of specimen fractures. FIB technology has helped a huge amount by making it possible to carve the specimen in ways that may improve survival. Conformal coatings on specimens after final shaping should add mechanical integrity and improve results, but this is still a developmental area. There are also efforts to use the information being received at the detector (composition at the apex, for example) to make smart decisions for controlling the evaporation conditions. These areas still need development, and there is no universal solution now for yield challenges in difficult specimens, but a very large range of materials run without much difficulty.

15.6.2 Reconstruction

The heterogeneous materials that usually are data yield challenges are usually also the ones for which reconstruction is less than ideal. If a data set is recorded, image distortions due to limitations of existing reconstruction algorithms for heterogeneous specimens can render the results compromised and even ineffective. A fundamental question is whether it is possible to largely eliminate distortions in reconstructions through either endogenous information (information contained in the atom probe data itself) or exogenous information (information obtained from external sources). Both approaches need to be explored, and there are efforts in the world on each as mentioned above in Sect. 15.2.11. There are major initiatives aimed at solving distortions through exogenous information which are described below in Sect. 15.6.6.

15.6.3 Detector Technology

The detector is the heart of an atom probe. The very first atom probe had to solve the challenge of detecting single atoms, which had never been done before [15.18]. For atom-probe tomography, the challenge is significantly greater: the extensive list of performance specifications in Table 15.1 illustrates the challenges. Position, timing, and detection efficiency are all essential characteristics. However, we need better. If a \({\mathrm{10}}\,{\mathrm{keV}}\) ion lands inside a channel in a microchannel plate, it will produce \(3\pm\sqrt{3}\) secondary electrons, which typically go on to be amplified by a factor of \(\mathrm{10^{5}}\). This means that we cannot distinguish whether a signal amplitude of \(\mathrm{2\times 10^{5}}\) electrons (or \(\mathrm{4\times 10^{5}}\) electrons) is from one ion or two. Multihit discrimination based on signal amplitude is not possible in this case.

With a delay-line detector, the signal propagates at a certain speed along the line, and the arrival time of the signal is used to infer the hit location along the line. The time width of the signal (called pulse-pair resolution) is large however, so that two hit signals must be separated by a large fraction of the line length to be recognized as two distinct pulses. Thus, since time is distance along the line, two pulses must be separated in either time or space by a few nanoseconds to be counted as two separate hits. This is a problem when two ions of the same isotope evaporate near each other at the same time from the surface of a specimen. There are cases where this is a problem like for boron in silicon [15.72, 15.74] or carbon in metal carbides [15.73].

A commercial atom probe achieves \({\mathrm{80}}\%\) detection efficiency today (CAMECA LEAP 5000S), but it is not likely to go much higher. To achieve \({\mathrm{100}}\%\) will require new technology. Superconducting detector technology is being pursued as way to achieve \({\mathrm{100}}\%\) detection efficiency [15.112]. This technology may also have the benefit that the pulse-pair resolution is finer, and the spatial interferences of pulses are very small. Both effects should lead to better multihit performance. It will be a few years before this technology is offered commercially, if at all, but the preliminary findings have been encouraging.

15.6.4 Combined Electron Tomography and Atom-Probe Tomography

There is an array of signals from (S)TEM that can complement atom-probe tomography including imaging, electron diffraction, electron energy-loss spectroscopy ( ), and energy-dispersive x-ray spectroscopy ( ). The first effort to combine the tomographic capabilities of both (S)TEM and APT on a single specimen was performed by Arslan et al [15.158] (Fig. 15.41a-d). This work highlighted one form of correlative microscopy for atom-probe tomography: imaging. In this work, a specimen of Al-\({\mathrm{3}}\,{\mathrm{at.\%}}\) Ag with Ag-rich precipitates was first imaged with electron tomography ( ) (Fig. 15.41a-db), and then analyzed with APT in a LEAP 3000 (Fig. 15.41a-dc). After reconstruction, the two tomographs were combined (Fig. 15.41a-dd). In this work, the {110} of Al were visible in the APT tomograph, and these were used as an internal length-scale calibration. Thus, the two tomographs had excellent spatial registry. It was possible to compare the precipitate sizes and shapes and deduce that different distortions were at play in each form of tomography. This comparison therefore yielded greater confidence in the outcome than could have been realized by either technique alone. It was even possible to see a small tilt difference between the two tomographs, which was attributed to specimen mounting differences in the two instruments. This early LEAP had a smaller field of view than later LEAPs, but the ET could complement it with a full field of view of the specimen. Neither technique, as practiced, had isotropic spatial resolution and the direction of lowest resolution in ET (due to the missing wedge) corresponded to a direction of high spatial resolution in LEAP and vice versa. Note that ET of needles can be performed without a missing wedge since the thickness is nominally constant in the observation direction, which is perpendicular to the long axis of the needle [15.159].

Fig. 15.41a-d

Combined atom probe tomography and electron tomography of an Al-\({\mathrm{3}}\,{\mathrm{at.\%}}\) Ag alloy with spheroidal precipitates. (a) STEM annular dark-field ( ) image, (b) Ag atom map of (a) from electron tomograph, (c) Ag atom map from atom probe tomography from the same specimen region as (a), and (d) two-dimensional () image of a combined tomograph where yellow dots are the Ag atoms from atom probe tomography and the fuchsia features are the Ag atom map from electron tomography. Reprinted from [15.158], with permission from Elsevier

Under the conditions that favor high-quality ET, EDS-based composition determinations are not optimized. The LEAP compositional data were of much higher quality. For example, a core–shell structure was observed readily in the LEAP data. Also, small Ag-rich clusters are readily observed and quantified in APT data, but are not even observed in (S)TEM.

15.6.5 Combined EDS Tomography and Atom-Probe Tomography

STEM-EDS tomography has progressed in the past five years with the development of multiple-detector, high-solid-angle EDS systems [15.161]. The signal improvements are always welcome and are especially useful for tomographic applications where speed is at a premium. Guo et al [15.160] have used this technology to combine STEM-EDS tomography with APT, as shown in Fig. 15.42, in a study of a spinodally decomposed alnico 8 magnetic alloy. Figure 15.42a,b is STEM-EDS tomographs which show an Fe-Co-rich \(\upalpha_{1}\) phase surrounded by an Ni-Al-rich \(\upalpha_{2}\) phase. Figure 15.42c,d shows the atom probe tomographs from the same volume. Note that the needle-shaped specimen received carbon contamination deposits during the STEM-EDS analysis, which was removed by \({\mathrm{2}}\,{\mathrm{kV}}\) FIB ion cleaning prior to APT.

Fig. 15.42

(a) A cropped alnico alloy reconstructed volume from STEM-EDS tomography. The pink-colored Fe isosurface differentiates \(\upalpha_{1}\) and \(\upalpha_{2}\) phases. (b) A \(90^{\circ}\) rotational view of the reconstruction shown in (a). (c) An atom probe tomography reconstruction of the alnico alloy with a \({\mathrm{30}}\,{\mathrm{at.\%}}\) Fe isosurface and \({\mathrm{10}}\,{\mathrm{at.\%}}\) Cu isosurface. Crystalline \(\langle 001\rangle\) directions were marked based on a previous electron backscatter diffraction measurement. Arrows point out \({\mathrm{5}}\,{\mathrm{nm}}\) secondary \(\upalpha_{1}\) precipitates. Two regions of interest are selected for further composition analysis. (d) A \(90^{\circ}\) rotational view of the reconstruction shown in (c). From [15.160], reproduced with permission

STEM-EDS tomography can provide analyses of larger volumes at higher speed than APT, which gives it an advantage in statistical precision for measurement of phase volume. However, APT provides higher spatial resolution and compositional sensitivity than STEM-EDS tomography. Small (\({\mathrm{5}}\,{\mathrm{nm}}\)) secondary \(\upalpha_{1}\) precipitates were found inside the \(\upalpha_{2}\) phase with APT that were not detected with STEM-EDS tomography (Fig. 15.42c). APT also detected \(1{-}2\,{\mathrm{nm}}\) Cu-rich clusters at the \(\upalpha_{1}/\upalpha_{2}\) interfaces (Fig. 15.42d). The spatial fidelity of STEM was used to advantage in adjusting the APT reconstruction parameters so that the {100} lattice spacing in the APT image is measured as \({\mathrm{0.30}}\,{\mathrm{nm}}\), which deviates only slightly from the established value of \({\mathrm{0.29}}\,{\mathrm{nm}}\). The {100} lattice spacing was observed to be continuous across the \(\upalpha_{1}/\upalpha_{2}\) interfaces. The authors conclude that:

The correlative STEM-EDS/APT tomography greatly advances 3-D structure characterization with less ambiguity than one technique alone and holds promise in future efforts to investigate nanoscale materials.

15.6.6 Integrated APT and (S)TEM

With the several examples above of correlative STEM-APT analyses, the results and efforts expended to achieve them beg the question of whether (S)TEM and APT should be combined into one instrument. Given that this would entail an increase in cost and complexity, we must consider what the benefits would be relative to using separate instruments serially. This question has been considered for some time, but has received particular attention in the past decade [15.100, 15.162, 15.163, 15.164, 15.98].

Specimens which are transported through the atmosphere are materially changed. We cannot expect to stitch together data sets from (S)TEM and APT without defects when the data contain oxidation and/or contamination. In the example above from Guo et al, a FIB was used to clean contamination off the needle surface prior to APT analysis. For the case where STEM is used to image the specimen apex shape multiple times during a serial STEM-APT experiment, the tip must be transported to the STEM and returned to the same spot in the APT if it is to resume evaporation as though nothing had happened. Ex-situ serial data recording experiments of this nature are being pursued by Baptiste Gault and Dierk Raabe at the Max-Planck-Institut für Eisenforschung in Düsseldorf, Germany, in cooperation with the author and CAMECA as phase I of a program to integrate STEM and APT. A cryo-ultrahigh-vacuum suitcase model VSN40S from Ferrovac GmbH, Zurich, will be used to transport specimens between a LEAP \(\mathrm{5000}\) and an FEI \({\mathrm{30}}\,{\mathrm{kV}}\) FIB/STEM with a cryo-stage. It is expected that experiments will require days of careful serial data recording. If phase I is successful, phase II of this project would build a dedicated LEAP-STEM. A project to build a dedicated LEAP-TEM is also being pursued by Rafal Dunin-Borkowski and Joachim Mayer of Forschungszentrum Jülich, and Dierk Raabe in cooperation with the author and CAMECA.

Serial imaging of the specimen apex is intended to provide needed shape information that will be used to reduce distortions in the APT reconstruction [15.162, 15.165, 15.98]. The analytical functions of STEM would be used to complement the atomic-scale compositional information of APT [15.100]. In addition to integration of the hardware operations, there is a need to:
  • Develop methods to use the specimen apex shape information to reduce distortions in the APT reconstructions. Haley et al [15.165] have developed a methodology that uses surface shape at sequential instants in time from an efficient surface tomography algorithm [15.166, 15.167] to compute back-projected ion trajectories from the detector to the specimen apex. This information would be used to produce correct reconstructions based on actual specimen shapes. Gorman, Ceguerra, Cairney, and Ringer (unpublished work, 2016) have recently made progress on an atomic-scale reconstruction method that relies on knowledge of the specimen apex shape before and after analysis.

  • Develop methods to interpolate the specimen apex shape between (S)TEM image recordings so that a continuous model of the specimen apex shape is available throughout the APT experiment. Haley et al [15.168, 15.169] have considered level-set theory for this purpose. Vurpillot [15.97] has recently explored phase field theory for this purpose.

  • Develop integrated data structures that facilitate concurrent analyses and exploitation of the synergies accrued. Efforts are underway to develop integrated data file structures. A workshop on data formats was held August 25 and 26, 2016, in Düsseldorf, Germany, at the Max-Planck-Institut für Eisenforschung to begin work on a unified data format for electron microscopy data, atom-probe tomography data, electron diffraction data, and computational materials modeling information. There is also an effort developing within the 3-DAM European Project for APT and STEM to address similar needs. These efforts will take a few years and will hopefully be merged to create a single standard.

Given the very strong synergies that exist between (S)TEM and APT, integrated instruments will no doubt become a commercial reality within the next decade.

15.7 Conclusions

Atom-probe tomography is like most scientific techniques: it has outstanding capabilities and it has its limitations. The capabilities that stand out are its unique combination of very high spatial resolution for analysis (\(<{\mathrm{0.2}}\,{\mathrm{nm}}\) locally in many specimens) with high analytical sensitivity (single atoms and parts-per-million fractions). Most inorganic materials can be analyzed in the atom probe today, and organic materials are on the horizon. The next decade should see major progress in efforts to analyze soft biological tissue. The trend toward the use of correlative analysis with (S)TEM and atom probe will continue, and combined instruments will make their debut in the early 2020s.

2017 is the 50th anniversary of the invention of the atom probe. The field has matured a great deal, especially in the past two decades. I think, however, that the best years are yet to come. With these developments will come eager users of the technology, and the field will grow and broaden markedly as a result. The early practitioners of atom probe can recall the hardware and physics challenges they faced and marvel at the progress they see today. But technological growth tends to be nonlinear, and new technologies are coming into the field from all directions, brought in by people from a variety of backgrounds. There are many positive factors currently steering the field toward greater achievements, and I see these as creating a perfect storm of development in the next few decades. When computational materials science is coupled with atomic-scale tomography, a complete description of matter will result. No atom will be able to hide from the casual observer. The next \(\mathrm{50}\) years will be atomic.

Notes

Acknowledgements

The author would like to acknowledge the collaborative efforts of many people in developing the concepts in this article. Dierk Raabe, Baptiste Gault, Gerhard Dehm, and Christina Scheu on Project Laplace at Max-Planck-Institut für Eisenforschung Düsseldorf; Dierk Raabe, Rafal Dunin-Borkowski, Joachim Mayer, and Max Haider on Project Tomo at Forschungszentrum Jülich; Simon P. Ringer, Michael K. Miller, Krishna Rajan, Ondrej Krivanek, and Niklas Dellby on the ATOM Project; Brian Gorman, David Dierks, Christoph Koch, and Wouter van den Broek on LEAP-STEM imaging; Robert McDermott and Joseph Suttle on superconducting detector development; and Jeff Shepard, David J. Larson, Katherine P. Rice, Ty J. Prosa, Brian P. Geiser, Robert Ulfig, Joseph H. Bunton, Tim Payne, Dan Lenz, and Ed Oltman at Cameca Instruments, Inc. John Panitz has helped immensely in correctly recounting some of the history of the early days at Pennsylvania State University with Professor Erwin W. Müller.

References

  1. W. Friedrich, P. Knipping, M. Laue: Phénomènes d'interférence des rayons de Röntgen, Radium 10, 47–57 (1913)CrossRefGoogle Scholar
  2. W.L. Bragg: The diffraction of short electromagnetic waves by a crystal, Proc. Camb. Philos. Soc. 17, 43–57 (1912)Google Scholar
  3. M. Eckert: Max von Laue and the discovery of x-ray diffraction 1912, Ann. Phys. 524, A83–A85 (2012)CrossRefGoogle Scholar
  4. L. de Broglie: Waves and quanta, Nature 112, 540 (1923)CrossRefGoogle Scholar
  5. H. Busch: Über die Wirkungsweise der Konzentrierungsspule bei der Braunschen Röhre, Arch. Elektrotech. 18, 583–594 (1927)CrossRefGoogle Scholar
  6. K. Bahadur: Experimental Investigation of Field Ion Emission, Ph.D. Thesis (Pennsylvania State Univ., State College 1955)Google Scholar
  7. E.W. Müller, K. Bahadur: Field ionization of gases at a metal surface and the resolution of the field ion microscope, Phys. Rev. 102, 624–631 (1956)CrossRefGoogle Scholar
  8. A.V. Crewe, J. Wall, J. Langmore: Visibility of single atoms, Science 168, 1338–1340 (1970)CrossRefGoogle Scholar
  9. E.W. Müller: Versuche zur Theorie der Elektronenemission unter der Einwirkung hoher Feldstärken, Z. Tech. Phys. 17, 412 (1936)Google Scholar
  10. E.W. Müller: Das Auflösungsvermögen des Feldelektronenmikroskops, Z. Phys. 120, 270 (1943)CrossRefGoogle Scholar
  11. E.W. Müller: Elektronenmikroskopische Beobachtungen von Feldkathoden, Z. Phys. 106, 541–550 (1937)CrossRefGoogle Scholar
  12. E.W. Müller: Das Feldionenmikroskop, Z. Phys. 131, 136–142 (1951)CrossRefGoogle Scholar
  13. A.J. Melmed: Recollections of Erwin Müller's laboratory: The development of FIM (1951–1956), Appl. Surf. Sci. 94/95, 17–25 (1996)CrossRefGoogle Scholar
  14. E.W. Müller: Resolution of the atomic structure of a metal surface by the field ion microscope, J. Appl. Phys. 27, 474–476 (1956)CrossRefGoogle Scholar
  15. M.K. Miller, J.A. Horton: Direct observation of boron segregation to line and planar defects in Ni3Al, J. Phys. Colloq. 48, 379–384 (1987)Google Scholar
  16. M.K. Miller, A. Cerezo, M.G. Hetherington, G.D.W. Smith: Atom Probe Field Ion Microscopy (Oxford Univ. Press, Oxford 1996)Google Scholar
  17. D.F. Barofsky: A personal retrospective on the origin of the time-of-flight atom probe, Microsc. Microanal. 23, 604–606 (2017)CrossRefGoogle Scholar
  18. E.W. Müller, J.A. Panitz, S.B. McLane: The atom-probe field ion microscope, Rev. Sci. Instrum. 39, 83–86 (1968)CrossRefGoogle Scholar
  19. A. Cerezo, G.D.W. Smith, A.R. Waugh: The FIM100—Performance of a commercial atom probe system, J. Phys. C 9, 329–335 (1984)Google Scholar
  20. J.A. Panitz: The 10 cm atom probe, Rev. Sci. Instrum. 44, 1034–1038 (1973)CrossRefGoogle Scholar
  21. J.A. Panitz: Imaging atom-probe mass spectroscopy, Prog. Surf. Sci. 8, 219–262 (1978)CrossRefGoogle Scholar
  22. M.K. Miller: The effects of local magnification and trajectory aberrations on atom probe analysis, J. Phys. 48, 565–570 (1987)CrossRefGoogle Scholar
  23. A.R. Waugh, C.H. Richardson, R. Jenkins: APFIM 200—A reflectron-based atom probe, Surf. Sci. 266, 501–505 (1992)CrossRefGoogle Scholar
  24. G.L. Kellogg, T.T. Tsong: Pulsed-laser atom-probe field-ion microscopy, J. Appl. Phys. 51, 1184–1194 (1980)CrossRefGoogle Scholar
  25. M.K. Miller: Atom-probe field ion microscopy. In: Microbeam Anal. Soc. Annu. Meet (San Francisco Press, Albuquerque 1986) pp. 343–347Google Scholar
  26. A. Cerezo, T.J. Godfrey, G.D.W. Smith: Application of a position-sensitive detector to atom probe microanalysis, Rev. Sci. Instrum. 59, 862–866 (1988)CrossRefGoogle Scholar
  27. A. Cerezo, T.J. Godfrey, G.D.W. Smith: Development and initial applications of a position-sensitive atom probe, J. Phys. Colloq. 49(C6), 25–30 (1988)CrossRefGoogle Scholar
  28. D. Blavette, B. Deconihout, A. Bostel, J.M. Sarrau, M. Bouet, A. Menand: The tomographic atom probe: A quantitative three-dimensional nanoanalytical instrument on an atomic scale, Rev. Sci. Instrum. 64, 2911–2919 (1993)CrossRefGoogle Scholar
  29. D. Blavette, A. Bostel, J.M. Sarrau, B. Deconihout, A. Menand: An atom probe for three-dimensional tomography, Nature 363, 432–435 (1993)CrossRefGoogle Scholar
  30. B. Deconihout, A. Bostel, P. Bas, S. Chambreland, L. Letellier, F. Danoix, D. Blavette: Investigation of some selected metallurgical problems with the tomographic atom probe, Appl. Surf. Sci. 76/77, 145–154 (1994)CrossRefGoogle Scholar
  31. O. Nishikawa, M. Kimoto: Toward a scanning atom probe—Computer simulation of electric field, Appl. Surf. Sci. 76/77, 424–430 (1994)CrossRefGoogle Scholar
  32. O. Nishikawa, M. Kimoto, M. Iwatsuki, Y. Ishikawa: Development of a scanning atom probe, J. Vac. Sci. Technol. B 13, 599–602 (1995)CrossRefGoogle Scholar
  33. T.F. Kelly, P.P. Camus, D.J. Larson, L.M. Holzman, S.S. Bajikar: On the many advantages of local-electrode atom probes, Ultramicroscopy 62, 29–42 (1996)CrossRefGoogle Scholar
  34. T.F. Kelly, D.J. Larson: Local electrode atom probes, Mater. Charact. 44, 59–85 (2000)CrossRefGoogle Scholar
  35. A. Cerezo, C.R.M. Grovenor, G.D.W. Smith: Pulsed laser atom probe analysis of III-V compound semiconductors, J. Phys. Colloq. 47(C2), 309–314 (1986)CrossRefGoogle Scholar
  36. A. Cerezo, C.R.M. Grovenor, G.D.W. Smith: Pulsed laser atom probe analysis of semiconductor materials, J. Microsc. 141, 155–170 (1986)CrossRefGoogle Scholar
  37. B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, B. Deconihout: Design of a femtosecond laser assisted tomographic atom probe, Rev. Sci. Instrum. 77, 043705 (2006)CrossRefGoogle Scholar
  38. J.H. Bunton, J.D. Olson, D. Lenz, T.F. Kelly: Advances in pulsed-laser atom probe: Instrument and specimen design for optimum performance, Microsc. Microanal. 13, 418–427 (2007)CrossRefGoogle Scholar
  39. A. Devaraj, D.E. Perea, J. Liu, L.M. Gordon, T.J. Prosa, P. Parikh, D.R. Diercks, S. Meher, R.P. Kolli, Y.S. Meng, S. Thevuthasan: Three-dimensional nanoscale characterisation of materials by atom probe tomography, Int. Mater. Rev. 63, 68–101 (2017)CrossRefGoogle Scholar
  40. M.K. Miller, R.G. Forbes: Atom-Probe Tomography: The Local Electrode Atom Probe, 1st edn. (Springer, Boston 2014)Google Scholar
  41. D.F. Barofsky, E.W. Müller: Mass spectrometric analysis of low temperature field evaporation, Surf. Sci. 10, 177–196 (1968)CrossRefGoogle Scholar
  42. E.W. Müller, J. Panitz: The Atom-Probe Field Ion Microscope (Abstract) (National Bureau of Standards, Washington 1967) p. 31Google Scholar
  43. P.H. Clifton, T.J. Gribb, S.S.A. Gerstl, R.M. Ulfig, D.J. Larson: Performance advantages of a modern, ultra-high mass resolution atom probe, Microsc. Microanal. 14, 454–455 (2008)CrossRefGoogle Scholar
  44. L. Currie: Limits for qualitative detection and quantitative determination, Anal. Chem. 40, 586–593 (1968)CrossRefGoogle Scholar
  45. T.T. Tsong: Instrumentation and techniques. In: Atom Probe Field Ion Microscopy (Cambridge Univ. Press, New York 1990) pp. 103–163CrossRefGoogle Scholar
  46. E. Oltman, T.F. Kelly, T.J. Prosa, D. Lawrence, D.J. Larson: Measuring contributions to mass resolving power in atom probe tomography, Microsc. Microanal. 17(S2), 754–755 (2011)CrossRefGoogle Scholar
  47. D.J. Larson, T.J. Prosa, R.M. Ulfig, B.P. Geiser, T.F. Kelly: Appendix D: Mass spectral performance. In: Local Electrode Atom Probe Tomography: A User's Guide (Springer, New York 2013) pp. 281–287CrossRefGoogle Scholar
  48. B. Gault, M.P. Moody, J.M. Cairney, S.P. Ringer: Atom Probe Microscopy (Springer, New York 2012)CrossRefGoogle Scholar
  49. W.P. Poschenrieder: Multiple-focusing time of flight mass spectrometers Part I. TOFMS with equal momentum acceleration, Int. J. Mass. Spectrom. Ion Phys. 6, 413–426 (1971)CrossRefGoogle Scholar
  50. W.P. Poschenrieder: Multiple-focusing time-of-flight mass spectrometers Part II. TOFMS with equal energy acceleration, Int. J. Mass Spectrom. Ion Phys. 9, 357–373 (1972)CrossRefGoogle Scholar
  51. B.A. Mamyrin, V.I. Karataev, D.V. Shmikk, V.A. Zagulin: The mass-reflectron, a new nonmagnetic time-of-flight mass spectrometer with high resolution, Sov. Phys. JETP 37, 45–48 (1973)Google Scholar
  52. A. Cerezo, T.J. Godfrey, S. Sijbrandij, G.D.W. Smith, P.J. Warren: Performance of an energy compensated three-dimensional atom probe, Rev. Sci. Instrum. 69, 49–58 (1998)CrossRefGoogle Scholar
  53. P. Panayi: Reflectron, US Patent 8134119 (2012)Google Scholar
  54. A. Cerezo, P.H. Clifton, S. Lozano-Perez, P. Panayi, G. Sha, G.D.W. Smith: Overview: Recent progress in three-dimensional atom probe instruments and applications, Microsc. Microanal. 13, 408–417 (2007)CrossRefGoogle Scholar
  55. M.K. Miller, G.D.W. Smith: An atom probe study of the anomalous field evaporation of alloys containing silicon, J. Vac. Sci. Technol. 19, 57–62 (1981)CrossRefGoogle Scholar
  56. R. Herschitz, D.N. Seidman: A quantitative atom-probe field-ion microscope study of the compositions of dilute Co(Nb) and Co(Fe) alloys, Surf. Sci. 130, 63–88 (1983)CrossRefGoogle Scholar
  57. J. Liu, T.T. Tsong: High resolution ion kinetic energy analysis of field emitted ions, J. Phys. Colloq. 49(C6), 61–66 (1988)Google Scholar
  58. J.A. Liddle, A. Norman, A. Cerezo, C.R.M. Grovenor: Pulsed laser atom probe analysis of ternary and quaternary III–V epitaxial layers, J. Phys. Colloq. 49, 509–514 (1988)CrossRefGoogle Scholar
  59. R. Schlesiger, C. Oberdorfer, R. Wurz, G. Greiwe, P. Stender, M. Artmeier, P. Pelka, F. Spaleck, G. Schmitz: Design of a laser-assisted tomographic atom probe at Münster University, Rev. Sci. Instrum. 81, 043703 (2010)CrossRefGoogle Scholar
  60. A. Cerezo, G.D.W. Smith, P.H. Clifton: Measurement of temperature rises in the femtosecond laser pulsed three-dimensional atom probe, Appl. Phys. Lett. 88, 154103 (2006)CrossRefGoogle Scholar
  61. F. Vurpillot, B. Gault, A. Vella, A. Bouet, B. Deconihout: Estimation of the cooling times for a metallic tip under laser illumination, Appl. Phys. Lett. 88, 094105 (2006)CrossRefGoogle Scholar
  62. A. Vella: On the interaction of an ultra-fast laser with a nanometric tip by laser assisted atom probe tomography: A review, Ultramicroscopy 132, 5–18 (2013)CrossRefGoogle Scholar
  63. T.F. Kelly, A. Vella, J.H. Bunton, J. Houard, E.P. Silaeva, J. Bogdanowicz, W. Vandervorst: Laser pulsing of field evaporation in atom probe tomography, Curr. Opin. Solid State Mater. Sci. 18, 81–89 (2014)CrossRefGoogle Scholar
  64. A. Cerezo, T.J. Godfrey, M. Huang, G.D.W. Smith: Design of a scanning atom probe with improved mass resolution, Rev. Sci. Instrum. 71, 3016–3023 (2000)CrossRefGoogle Scholar
  65. A. Cerezo, D. Vaumousse: Numerical modelling of mass resolution in a scanning atom probe, Ultramicroscopy 89, 155–161 (2001)CrossRefGoogle Scholar
  66. F. Vurpillot, C. Oberdorfer: Modeling atom probe tomography: A review, Ultramicroscopy 159(2), 202–216 (2015)CrossRefGoogle Scholar
  67. L. Zhao, A. Normand, J. Houard, I. Blum, F. Delaroche, F. Vurpillot: Numeric modeling of synchronous laser pulsing and voltage pulsing field evaporation, arXiv:1607.02127 [physics.ins-det] (2016)Google Scholar
  68. T.F. Kelly, D.J. Larson: The second revolution in atom probe tomography, MRS Bulletin 37, 150–158 (2012)CrossRefGoogle Scholar
  69. H. Keller, G. Klingelhöfer, E. Kankeleit: A position sensitive microchannelplate detector using a delay line readout anode, Nucl. Instrum. Methods Phys. Res. A 258, 221–224 (1987)CrossRefGoogle Scholar
  70. G. Da Costa, F. Vurpillot, A. Bostel, A. Bouet, B. Deconihout: Design of a delay-line position-sensitive detector with improved performance, Rev. Sci. Instrum. 76, 013304 (2004)CrossRefGoogle Scholar
  71. M.K. Miller, K.F. Russell: Performance of a local electrode atom probe, Surf. Interface Anal. 39, 262–267 (2007)CrossRefGoogle Scholar
  72. P. Ronsheim, P. Flaitz, M. Hatzistergos, C. Molella, K. Thompson, R. Alvis: Impurity measurements in silicon with D-SIMS and atom probe tomography, Appl. Surf. Sci. 255, 1547–1550 (2008)CrossRefGoogle Scholar
  73. M. Thuvander, J. Weidow, J. Angseryd, L.K.L. Falk, F. Liu, M. Sonestedt, K. Stiller, H.O. Andren: Quantitative atom probe analysis of carbides, Ultramicroscopy 111, 604–608 (2011)CrossRefGoogle Scholar
  74. G. Da Costa, H. Wang, S. Duguay, A. Bostel, D. Blavette, B. Deconihout: Advance in multi-hit detection and quantization in atom probe tomography, Rev. Sci. Instrum. 83, 123709 (2012)CrossRefGoogle Scholar
  75. J. Takahashi, K. Kawakami, Y. Kobayashia, T. Tarui: The first direct observation of hydrogen trapping sites in TiC precipitation-hardening steel through atom probe tomography, Scr. Mater. 63, 261–264 (2010)CrossRefGoogle Scholar
  76. H. Sepehri-Amin, T. Ohkubo, T. Nishiuchi, S. Hirosawa, K. Hono: Quantitative laser atom probe analyses of hydrogenation-disproportionated Nd-Fe-B powders, Ultramicroscopy 111, 615–618 (2011)CrossRefGoogle Scholar
  77. R. Calder, G. Lewin: Reduction of stainless-steel outgassing in ultra-high vacuum, Br. J. Appl. Phys. 18, 1459 (1967)CrossRefGoogle Scholar
  78. J. Takahashi, K. Kawakami, T. Tarui: Direct observation of hydrogen-trapping sites in vanadium carbide precipitation steel by atom probe tomography, Scr. Mater. 67, 213–216 (2012)CrossRefGoogle Scholar
  79. P. Bas, A. Bostel, B. Deconihout, D. Blavette: A general protocol for the reconstruction of 3-D atom probe data, Appl. Surf. Sci. 87/88, 298–304 (1995)CrossRefGoogle Scholar
  80. D.J. Larson, T.J. Prosa, R.M. Ulfig, B.P. Geiser, T.F. Kelly: Local Electrode Atom Probe Tomography: A User's Guide (Springer, New York 2013)CrossRefGoogle Scholar
  81. B. Gault, D. Haley, F. de Geuser, M.P. Moody, E.A. Marquis, D.J. Larson, B.P. Geiser: Advances in the reconstruction of atom probe tomography data, Ultramicroscopy 111, 448–457 (2011)CrossRefGoogle Scholar
  82. J. Ge: Interfacial Adhesion in Metal/Polymer Systems for Electronics, Ph.D. Thesis (Helsinki Univ. Technology, Helsinki 2003)Google Scholar
  83. D.J. Larson, B. Gault, B.P. Geiser, F. De Geuser, F. Vurpillot: Atom probe tomography spatial reconstruction: Status and directions, Curr. Opin. Solid State Mater. Sci. 17, 236–247 (2013)CrossRefGoogle Scholar
  84. D.J. Larson, B.P. Geiser, T.J. Prosa, S.S.A. Gerstl, D.A. Reinhard, T.F. Kelly: Improvements in planar feature reconstructions in atom probe tomography, J. Microsc. 243, 15–30 (2011)CrossRefGoogle Scholar
  85. D.J. Larson, B.P. Geiser, T.J. Prosa, R. Ulfig, T.F. Kelly: Non-tangential continuity reconstruction in atom probe tomography data, Microsc. Microanal. 17, 740–741 (2011)CrossRefGoogle Scholar
  86. N. Rolland, D.J. Larson, B.P. Geiser, S. Duguay, F. Vurpillot, D. Blavette: An analytical model accounting for tip shape evolution during atom probe analysis of heterogeneous materials, Ultramicroscopy 159, 195–201 (2015)CrossRefGoogle Scholar
  87. F. Vurpillot, W. Lefebvre, J.M. Cairney, C. Oberdorfer, B.P. Geiser, K. Rajan: Advanced volume reconstruction and data mining methods in atom probe tomography, MRS Bulletin 41, 46–51 (2016)CrossRefGoogle Scholar
  88. F. Vurpillot, B. Gault, B.P. Geiser, D.J. Larson: Reconstructing atom probe data: A review, Ultramicroscopy 132, 19–30 (2013)CrossRefGoogle Scholar
  89. D. Beinke, C. Oberdorfer, G. Schmitz: Towards an accurate volume reconstruction in atom probe tomography, Ultramicroscopy 165, 34–41 (2016)CrossRefGoogle Scholar
  90. B. Loberg, H. Norden: Observations of the field-evaporation end form of tungsten, Ark. Fys. 39, 383–395 (1968)Google Scholar
  91. J.M. Walls, H.N. Southworth: Magnification in the field-ion microscope, J. Phys. D 12, 657–667 (1979)CrossRefGoogle Scholar
  92. G.S. Gipson, H.C. Eaton: The electric field distribution in the field ion microscope as a function of specimen shank, J. Appl. Phys. 51, 5537–5539 (1980)CrossRefGoogle Scholar
  93. F. Vurpillot, A. Bostel, D. Blavette: The shape of field emitters and the ion trajectories in three-dimensional atom probes, J. Microsc. 196, 332–336 (1999)CrossRefGoogle Scholar
  94. E.A. Marquis, B.P. Geiser, T.J. Prosa, D.J. Larson: Evolution of tip shape during field evaporation of complex multilayer structures, J. Microsc. 241, 225–233 (2011)CrossRefGoogle Scholar
  95. S. Du, T. Burgess, S.T. Loi, B. Gault, Q. Gao, P. Bao, L. Li, X. Cui, W.K. Yeoh, H.H. Tan, C. Jagadish, S.P. Ringer, R. Zheng: Full tip imaging in atom probe tomography, Ultramicroscopy 124, 96–101 (2013)CrossRefGoogle Scholar
  96. J.H. Lee, B.H. Lee, Y.T. Kim, J.J. Kim, S.Y. Lee, K.P. Lee, C.G. Park: Study of vertical Si/SiO2 interface using laser-assisted atom probe tomography and transmission electron microscopy, Micron 58, 32–37 (2014)CrossRefGoogle Scholar
  97. F. Vurpillot: Private Communication, Université de Rouen (2016)Google Scholar
  98. T.F. Kelly, M.K. Miller, K. Rajan, S.P. Ringer: Atomic-scale tomography: A 2020 vision, Microsc. Microanal. 19, 652–664 (2013)CrossRefGoogle Scholar
  99. W. Lefebvre, D. Hernandez-Maldonado, F. Moyon, F. Cuvilly, C. Vaudolon, D. Shinde, F. Vurpillot: HAADF-STEM atom counting in atom probe tomography specimens: Towards quantitative correlative microscopy, Ultramicroscopy 159, 403–412 (2015)CrossRefGoogle Scholar
  100. T.F. Kelly: Atomic-scale analytical tomography, Microsc. Microanal. 23, 34–45 (2017)CrossRefGoogle Scholar
  101. B.P. Geiser, T.F. Kelly, D.J. Larson, J. Schneir, J.P. Roberts: Spatial distribution maps for atom probe tomography, Microsc. Microanal. 13, 437–447 (2007)CrossRefGoogle Scholar
  102. B. Gault, W. Yang, K.R. Ratinac, R. Zheng, F. Braet, S.P. Ringer: Atom probe microscopy of self-assembled monolayers: Preliminary results, Langmuir 26, 5291–5294 (2010)CrossRefGoogle Scholar
  103. A. Breen, M.P. Moody, B. Gault, A.V. Ceguerra, K.Y. Xie, S. Du, S.P. Ringer: Spatial decomposition of molecular ions within 3-D atom probe reconstructions, Ultramicroscopy 132, 92–99 (2013)CrossRefGoogle Scholar
  104. T. Boll, T. Al-Kassab, Y. Yuan, Z.G. Liu: Investigation of the site occupation of atoms in pure and doped TiAl/Ti3Al intermetallic, Ultramicroscopy 107, 796–801 (2007)CrossRefGoogle Scholar
  105. T.F. Kelly, B.P. Geiser, D.J. Larson: Definition of spatial resolution in atom probe tomography, Microsc. Microanal. 13, 1604–1605 (2007)Google Scholar
  106. T.F. Kelly, E. Voelkl, B.P. Geiser: Practical determination of spatial resolution in atom probe tomography, Microsc. Microanal. 15, 12–13 (2009)CrossRefGoogle Scholar
  107. B. Gault, M.P. Moody, F. De Geuser, D. Haley, L.T. Stephenson, S.P. Ringer: Origin of the spatial resolution in atom probe microscopy, Appl. Phys. Lett. 95, 034103 (2009)CrossRefGoogle Scholar
  108. F. Vurpillot, G. Da Costa, A. Menand, D. Blavette: Structural analyses in three-dimensional atom probe: A fourier transform approach, J. Microsc. 203, 295–302 (2001)CrossRefGoogle Scholar
  109. L.T. Stephenson, M.P. Moody, P.V. Liddicoat, S.P. Ringer: New techniques for the analysis of fine-scaled clustering phenomena within atom probe tomography (APT) data, Microsc. Microanal. 13, 448–463 (2007)CrossRefGoogle Scholar
  110. G.C. Hilton, J.M. Martinis, D.A. Wollman, K.D. Irwin, L.L. Dulcie, D. Gerber, P.M. Gillevet, D. Twerenbold: Impact energy measurement in time-of-flight mass spectrometry with cryogenic microcalorimeters, Nature 391, 672–675 (1998)CrossRefGoogle Scholar
  111. T.F. Kelly: Kinetic-energy discrimination for atom probe tomography, Micros. Microanal. 17, 1–14 (2011)CrossRefGoogle Scholar
  112. J.R. Suttle, T.F. Kelly, R.F. McDermott: A superconducting ion detection scheme for atom probe tomography. In: Atom Probe Tomogr. Microsc., Gyeongju (2016)Google Scholar
  113. T.J. Prosa, B.P. Geiser, D. Lawrence, D. Olson, D.J. Larson: Developing detection efficiency standards for atom probe tomography, Proc. SPIE 9173, 917307 (2014)CrossRefGoogle Scholar
  114. B. Gault, D.W. Saxey, M.W. Ashton, S.B. Sinnott, A.N. Chiaramonti, M.P. Moody, D.K. Schreiber: Behavior of molecules and molecular ions near a field emitter, New J. Phys. 18, 033031 (2016)CrossRefGoogle Scholar
  115. D.W. Saxey: Correlated ion analysis and the interpretation of atom probe mass spectra, Ultramicroscopy 111, 473–479 (2011)CrossRefGoogle Scholar
  116. A.J. Melmed: The art and science and other aspects of making sharp tips, J. Vac. Sci. Technol. B 9, 601–609 (1991)CrossRefGoogle Scholar
  117. W. Lefebvre, F. Vurpillot, X. Sauvage: Atom Probe Tomography: Put Theory into Practice (Academic Press, London 2016)Google Scholar
  118. A.R. Waugh, S. Payne, G.M. Worrall, G.D.W. Smith: In situ ion milling of field ion specimens using a liquid metal ion source, J. Phys. Colloq. 45, 207–209 (1984)CrossRefGoogle Scholar
  119. K.B. Alexander, P. Angelini, M.K. Miller: Precision ion milling of field-ion specimens, J. Phys. Colloq. 50, 549–554 (1989)CrossRefGoogle Scholar
  120. D.J. Larson, M.K. Miller, R.M. Ulfig, R.J. Matyi, P.P. Camus, T.F. Kelly: Field ion specimen preparation from near-surface regions, Ultramicroscopy 73, 273–278 (1998)CrossRefGoogle Scholar
  121. D.J. Larson, R.L. Martens, T.F. Kelly, M.K. Miller, N. Tabat: Atom probe analysis of planar multilayer structures, J. Appl. Phys. 87, 5989–5991 (2000)CrossRefGoogle Scholar
  122. M.K. Miller, K.F. Russell, G.B. Thompson: Strategies for fabricating atom probe specimens with a dual beam FIB, Ultramicroscopy 102, 287–298 (2005)CrossRefGoogle Scholar
  123. M.K. Miller, K.F. Russell: Atom probe specimen preparation with a dual beam SEM/FIB miller, Ultramicroscopy 107, 761–766 (2007)CrossRefGoogle Scholar
  124. M.K. Miller, K.F. Russell, K. Thompson, R. Alvis, D.J. Larson: Review of atom probe FIB-based specimen preparation methods, Microsc. Microanal. 13, 428–436 (2007)CrossRefGoogle Scholar
  125. K. Thompson, D.J. Lawrence, D.J. Larson, J.D. Olson, T.F. Kelly, B. Gorman: In-situ site-specific specimen preparation for atom probe tomography, Ultramicroscopy 107, 131–139 (2007)CrossRefGoogle Scholar
  126. T.J. Prosa, D.J. Larson: Modern focused-ion-beam-based site-specific specimen preparation for atom probe tomography, Microsc. Microanal. 23, 194–209 (2017)CrossRefGoogle Scholar
  127. D.J. Larson, T.J. Prosa, D. Lawrence, B.P. Geiser, C.M. Jones, T.F. Kelly: Atom probe tomography for microelectronics. In: Handbook of Instrumentation and Techniques for Semiconductor Nanostructure Characterization, ed. by R. Haight, F. Ross, J. Hannon (World Scientific, London 2011) pp. 407–477CrossRefGoogle Scholar
  128. M. Kuzmina, M. Herbig, D. Ponge, S. Sandlobes, D. Raabe: Linear complexions: Confined chemical and structural states at dislocations, Science 349, 1080–1083 (2015)CrossRefGoogle Scholar
  129. K.P. Rice, Y. Chen, T.J. Prosa, D.J. Larson: Implementing transmission electron backscatter diffraction for atom probe tomography, Microsc. Microanal. 22, 583–588 (2016)CrossRefGoogle Scholar
  130. O.C. Hellman, J.A. Vandenbroucke, J. Rusing, D. Isheim, D.N. Seidman: Analysis of three-dimensional atom-probe data by the proximity histogram, Microsc. Microanal. 6, 437–444 (2000)CrossRefGoogle Scholar
  131. M. Tang, W.C. Carter, R.M. Cannon: Grain boundary transitions in binary alloys, Phys. Rev. Lett. 97, 075502 (2006)CrossRefGoogle Scholar
  132. B. Gault, M.P. Moody, J.M. Cairney, S.P. Ringer: Atom probe crystallography, Mater. Today 15, 378–386 (2012)CrossRefGoogle Scholar
  133. D.R. Diercks, J. Tong, H. Zhu, R. Kee, G. Baure, J.C. Nino, R. O'Hayre, B.P. Gorman: Three-dimensional quantification of composition and electrostatic potential at individual grain boundaries in doped ceria, J. Mater. Chem. A 4, 5167–5175 (2016)CrossRefGoogle Scholar
  134. S.A. Wilde, J.W. Valley, W.H. Peck, C.M. Graham: Evidence from detrital zircons for the existence of continental crust and oceans on the Earth 4.4 Gyr ago, Nature 409, 175–178 (2001)CrossRefGoogle Scholar
  135. J. Valley, A.J. Cavosie, T. Ushikubo, D.A. Reinhard, D. Snoeyenbos, D. Lawrence, D.J. Larson, P.H. Clifton, T.F. Kelly, A. Strickland, S. Wilde, D. Moser: Hadean age for a post-magma-ocean zircon confirmed by atom-probe tomography, Nat. Geosci. 219, 219–223 (2014)CrossRefGoogle Scholar
  136. T.F. Kelly, D.J. Larson, K. Thompson, R.L. Alvis, J.H. Bunton, J.D. Olson, B.P. Gorman: Atom probe tomography of electronic materials, Annu. Rev. Mater. Res. 37, 681–727 (2007)CrossRefGoogle Scholar
  137. D.J. Larson, D. Lawrence, W. Lefebvre, D. Olson, T.J. Prosa, D.A. Reinhard, R.M. Ulfig, P.H. Clifton, J.H. Bunton, D. Lenz, L. Renaud, I. Martin, T.F. Kelly: Toward atom probe tomography of microelectronic devices, J. Phys. Conf. Ser. 326, 012030 (2011)CrossRefGoogle Scholar
  138. D. Blavette, S. Duguay: Atom probe tomography in nanoelectronics, Eur. Phys. J. Appl. Phys. 68, 10101 (2014)CrossRefGoogle Scholar
  139. M.A. Khan, S.P. Ringer, R. Zheng: Atom probe tomography on semiconductor devices, Adv. Mater. Interfaces 3, 1500713 (2016)CrossRefGoogle Scholar
  140. K. Inoue, H. Takamizawa, K. Kitamoto, J. Kato, T. Miyagi, Y. Nakagawa, N. Kawasaki, N. Sugiyama, H. Hashimoto, Y. Shimizu, T. Toyama, Y. Nagai, A. Karen: Three-dimensional elemental analysis of commercial 45 nm node device with high-k/metal gate stack by atom probe tomography, Appl. Phys. Express 4, 116601 (2011)CrossRefGoogle Scholar
  141. K. Inoue, A.K. Kambham, D. Mangelinck, D. Lawrence, D.J. Larson: Atom-probe-tomographic studies on silicon-based semiconductor devices, Microsc. Today 20, 38–44 (2012)CrossRefGoogle Scholar
  142. K. Inoue, H. Takamizawa, Y. Shimizu, F. Yano, T. Toyama, A. Nishida, T. Mogami, K. Kitamoto, T. Miyagi, J. Kato, S. Akahori, N. Okada, M. Kato, H. Uchida, Y. Nagai: Three-dimensional dopant characterization of actual metal–oxide–semiconductor devices of 65 nm node by atom probe tomography, Appl. Phys. Express 6, 046502 (2013)CrossRefGoogle Scholar
  143. L. Rigutti, L. Mancini, D. Hernández-Maldonado, W. Lefebvre, E. Giraud, R. Butté, J.F. Carlin, N. Grandjean, D. Blavette, F. Vurpillot: Statistical correction of atom probe tomography data of semiconductor alloys combined with optical spectroscopy: The case of Al0.25Ga0.75N, J. Appl. Phys. 119, 105704 (2016)CrossRefGoogle Scholar
  144. E.W. Müller: Sichtbarmachung der Phthalocyaninmolekel mit dem Feldelektronenmikroscop, Naturwissenschaften 37, 333 (1950)CrossRefGoogle Scholar
  145. E.W. Müller: Die Sichbarmachung einzelner Atome und Moleküle im Feldelektronenmikroskop, Z. Naturforsch. 5, 473 (1950)Google Scholar
  146. E.W. Müller: Feldemission. In: Springer Tracts in Modern Physics, Vol. 27, ed. by F. Hund, P. Harteck, W. Bothe (Springer, Berlin, Heidelberg 1953) pp. 290–360Google Scholar
  147. J.A. Panitz, I. Giaever: Ferritin deposition on field-emitter tips, Ultramicroscopy 6, 3–6 (1981)CrossRefGoogle Scholar
  148. J.A. Panitz: Point-projection imaging of unstained ferritin clusters, Ultramicroscopy 7, 241–248 (1982)CrossRefGoogle Scholar
  149. T.F. Kelly, O. Nishikawa, J.A. Panitz, T.J. Prosa: Prospects for nanobiology with atom-probe tomography, MRS Bulletin 34, 744–749 (2009)CrossRefGoogle Scholar
  150. L.M. Gordon, D. Joester: Nanoscale chemical tomography of buried organic-inorganic interfaces in the chiton tooth, Nature 469, 194–197 (2011)CrossRefGoogle Scholar
  151. L.M. Gordon, L. Tran, D. Joester: Atom probe tomography of apatites and bone-type mineralized tissues, ACS Nano 6, 10667–10675 (2012)CrossRefGoogle Scholar
  152. L.M. Gordon, D. Joester: Mapping residual organics and carbonate at grain boundaries and the amorphous interphase in mouse incisor enamel, Front. Physiol. 6, 57 (2015)CrossRefGoogle Scholar
  153. T.J. Prosa, M. Greene, T.F. Kelly, J. Fu, K. Narayan, S. Subramaniam: Atom probe tomography of mammalian cells: Advances in specimen preparation, Microsc. Microanal. 16, 482–483 (2010)CrossRefGoogle Scholar
  154. T.J. Prosa, S.K. Keeney, T.F. Kelly: Field evaporation of octadecanethiol, Microsc. Microanal. 15(S2), 300–301 (2009)CrossRefGoogle Scholar
  155. T.J. Prosa, S.K. Keeney, T.F. Kelly: Atom probe tomography analysis of poly(3-alkylthiophene)s, J. Microsc. 237, 155–167 (2010)CrossRefGoogle Scholar
  156. D.E. Perea, J. Liu, J. Bartrand, Q. Dicken, S.T. Thevuthasan, N.D. Browning, J.E. Evans: Atom probe tomographic mapping directly reveals the atomic distribution of phosphorus in resin embedded ferritin, Sci. Rep. 6, 22321 (2016)CrossRefGoogle Scholar
  157. T.J. Prosa, T.F. Kelly: Development of a Cryo-Transport System for Introduction of Frozen Specimens into a LEAP, Internal Report (CAMECA Instruments, Madison 2007)Google Scholar
  158. I. Arslan, E.A. Marquis, M. Homer, M.A. Hekmaty, N.C. Bartelt: Towards better 3-D reconstructions by combining electron tomography and atom-probe tomography, Ultramicroscopy 108, 1579–1585 (2008)CrossRefGoogle Scholar
  159. N. Kawase, M. Kato, H. Nishioka, H. Jinnai: Transmission electron microtomography without the ‘‘missing wedge'' for quantitative structural analysis, Ultramicroscopy 107, 8–15 (2007)CrossRefGoogle Scholar
  160. W. Guo, B.T. Sneed, L. Zhou, W. Tang, M.J. Kramer, D.A. Cullen, J.D. Poplawsky: Correlative energy-dispersive x-ray spectroscopic tomography and atom probe tomography of the phase separation in an alnico 8 alloy, Microsc. Microanal. 22, 1251–1260 (2016)CrossRefGoogle Scholar
  161. H.S. von Harrach, P. Dona, B. Freitag, H. Soltau, A. Niculae, M. Rohde: An integrated multiple silicon drift detector system for transmission electron microscopes, J. Phys. Conf. Ser. 241, 012015 (2010)CrossRefGoogle Scholar
  162. T.F. Kelly, M.K. Miller, K. Rajan, S.P. Ringer, A.Y. Borisevich, N. Dellby, O.L. Krivanek: Toward atomic-scale tomography: The ATOM project, Microsc. Microanal. 17(S2), 708–709 (2011)CrossRefGoogle Scholar
  163. B.P. Gorman, J.D. Shepard, R. Kirchhofer, J.D. Olson, T.F. Kelly: Development of atom probe tomography with in-situ STEM imaging and diffraction, Microsc. Microanal. 17, 710–711 (2011)CrossRefGoogle Scholar
  164. M.K. Miller, T.F. Kelly, K. Rajan, S.P. Ringer: The future of atom probe tomography, Mater. Today 15, 158–165 (2012)CrossRefGoogle Scholar
  165. D. Haley, T. Petersen, S.P. Ringer, G.D.W. Smith: Atom probe trajectory mapping using experimental tip shape measurements, J. Microsc. 244, 170–180 (2011)CrossRefGoogle Scholar
  166. T.C. Petersen, S.P. Ringer: An electron tomography algorithm for reconstructing 3-D morphology using surface tangents of projected scattering interfaces, Comput. Phys. Commun. 181, 676–682 (2010)CrossRefGoogle Scholar
  167. T.C. Petersen, S.P. Ringer: Electron tomography using a geometric surface-tangent algorithm: Application to atom probe specimen morphology, J. Appl. Phys. 105, 103518 (2009)CrossRefGoogle Scholar
  168. D. Haley, M.P. Moody, G.D.W. Smith: Level set methods for modelling field evaporation in atom probe, Microsc. Microanal. 19, 1709–1717 (2013)CrossRefGoogle Scholar
  169. D. Haley, P.A.J. Bagot, M.P. Moody: Extending continuum models for atom probe simulation, Mater. Charact. 146, 299–306 (2018)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Steam Instruments, Inc.Madison, WIUSA

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